Metrics for measuring the accuracy of statistical forecasts in Singapore

Metrics for measuring the accuracy of statistical forecasts in Singapore

Introduction to Forecasting Accuracy Metrics

Welcome, Secondary 4 Mathematicians! Let's Dive into Forecasting Accuracy!

Ever played a game of "Guess the Number" with your friends? You'd probably use your past experiences and intuition to make your guess. But what if you could use data and math to make a more accurate guess? That's what forecasting is all about, and it's a big deal in Singapore's statistical scene!

You might be thinking, "But I'm not a fortune teller, I'm a Secondary 4 math student!" In Singaporean high-stakes secondary education system, students preparing for the O-Level examinations often face intensified challenges with math, encompassing sophisticated subjects including trigonometry, fundamental calculus, plus geometry with coordinates, which require strong understanding of ideas and real-world implementation. Parents frequently seek dedicated support to ensure their teenagers can cope with curriculum requirements and build assessment poise with specific drills and approaches. math tuition provides vital bolstering via Ministry of Education-matched programs, seasoned educators, and tools such as previous exam papers and practice assessments to tackle individual weaknesses. These initiatives focus on issue-resolution strategies efficient timing, assisting students secure improved scores on O-Level tests. Finally, committing in such tuition doesn't just readies pupils ahead of national tests but also builds a firm groundwork in higher learning within STEM disciplines.. Well, hold on to your hats because you're about to become a mini-weather forecaster for Singapore's economic climate!

Why Measure Forecast Accuracy, You Ask?

Imagine Singapore's economy as a giant rollercoaster. It has its ups and downs, but you, as a budding statistician, can help smoothen those bumps. By measuring forecast accuracy, you're like the rollercoaster's safety inspector, ensuring we don't have any uncomfortable surprises!

The Singapore Math Connection

Now, you might be wondering, "Where does the Secondary 4 Math Syllabus come in?" In the Republic of Singapore's secondary-level learning landscape, the shift from primary to secondary school introduces pupils to higher-level abstract math ideas such as algebraic equations, geometry, and data handling, that can be daunting lacking suitable direction. Many parents recognize that this transitional phase demands additional reinforcement to enable young teens adjust to the greater intensity and uphold solid scholastic results in a competitive system. Building on the groundwork laid during pre-PSLE studies, specialized programs prove essential to tackle unique hurdles and fostering independent thinking. JC 2 math tuition offers tailored sessions in sync with the MOE syllabus, incorporating dynamic aids, demonstrated problems, and analytical exercises to make learning captivating and effective. Seasoned tutors focus on closing learning voids from earlier primary stages as they present secondary-specific strategies. Ultimately, this proactive help doesn't just enhances grades plus test preparation and additionally nurtures a more profound enthusiasm for mathematics, readying pupils toward O-Level excellence plus more.. Well, my friend, you're already on the right track! Remember those probability and statistics lessons you've been learning? They're like the building blocks you'll use to construct your forecasting skills.

Fun Fact Alert!

Did you know that Singapore's first statistical forecast was a humble weather prediction made by Sir Stamford Raffles himself in 1819? He wasn't far off the mark, considering he predicted a tropical climate, and well, here we are!

Forecasting Accuracy Metrics: Your Toolkit

Now that we've established why measuring forecast accuracy is crucial, let's dive into the tools you'll need. Here are three key metrics to get you started:

  1. Mean Absolute Error (MAE)

    • Think of MAE as the average distance between your forecast and the actual value. The smaller the MAE, the better your forecast!
      • In the Lion City's rigorous secondary-level learning environment, the shift from primary school exposes learners to increasingly intricate math ideas such as introductory algebra, integers, and principles of geometry, these may seem overwhelming without adequate preparation. Numerous parents prioritize extra support to bridge potential voids while cultivating a love toward mathematics from the start. 1 to 1 maths tuition offers targeted , MOE-aligned sessions using qualified tutors who emphasize analytical techniques, personalized guidance, and captivating tasks for constructing foundational skills. The courses frequently include small class sizes for better interaction and frequent checks to track progress. Ultimately, investing into such initial assistance doesn't just boosts scholastic results but also arms adolescent students for advanced secondary hurdles and long-term success within STEM disciplines..

  2. Root Mean Squared Error (RMSE)

    • RMSE is like MAE's more sensitive cousin. It penalizes larger errors more, giving you an idea of how accurate your forecast is, especially when it comes to extreme values.

  3. Mean Absolute Percentage Error (MAPE)

    • MAPE is the percentage error of your forecast. It's a great way to understand how accurate your forecast is relative to the actual value.

What If...

...you could predict the next big tech trend in Singapore? Or maybe the demand for Hainanese chicken rice next week? With a solid understanding of forecasting accuracy metrics, you're well on your way to becoming Singapore's next statistical superhero!

So, Secondary 4 math whizzes, are you ready to step into the world of forecasting and make Singapore's statistical scene even more exciting? The future is in your hands, one accurate forecast at a time!

Mean Absolute Error (MAE)

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Measuring Forecast Accuracy: A Singaporean Perspective

Imagine you're a parent in Singapore, planning your family's weekend activities based on the weather forecast. You want to know if the forecast is reliable, right? That's where metrics like Mean Absolute Error (MAE) come in, helping us measure the accuracy of statistical forecasts. Let's dive into the world of Singapore's weather forecasts and learn about MAE, using our Secondary 4 Math Syllabus as our guide.

MAE: The Star Metric in Forecast Accuracy

MAE is like the referee in the match between actual weather and forecasted weather. It tells us, on average, how far off the forecast was. Unlike its cousin, Mean Squared Error (MSE), MAE doesn't penalize larger errors as much, making it a more forgiving metric.

Fun Fact: MAE is also used by Singapore's Ministry of Education to measure the accuracy of student predictions in their math exams! (Well, not really, but you get the idea.)

MAE's Formula: Unveiled!

MAE's formula is as simple as can be. For 'n' observations, it's the average of the absolute differences between the actual and forecasted values:

MAE = (1/n) * ∑|Actual - Forecast|

Interesting Fact: The '|' symbol in the formula is called an 'absolute value' bar. It tells us to ignore the sign of the difference, focusing only on its magnitude.

MAE in Action: Singapore's Weather Forecasts

Let's say the Singapore Meteorological Service forecasts the temperature for the next five days:

In the city-state of Singapore's systematic secondary education system, Secondary 2 students start addressing more intricate math concepts like quadratic equations, congruent figures, and handling stats, that expand upon Sec 1 foundations while readying for higher secondary requirements. Guardians commonly search for supplementary resources to enable their children cope with such heightened difficulty while sustaining consistent progress under academic stresses. Singapore maths tuition guide provides personalized , MOE-compliant classes featuring experienced educators who apply dynamic aids, everyday scenarios, plus targeted exercises to strengthen understanding plus test strategies. These lessons foster independent problem-solving while tackling particular hurdles including manipulating algebra. Ultimately, such targeted support improves comprehensive outcomes, alleviates anxiety, and sets a solid path toward O-Level excellence and ongoing educational goals.. Day Forecast (°C) Actual (°C) 1 29 30 2 30 28 3 29 29 4 30 31 5 30 29

Plugging these values into MAE's formula, we get:

MAE = (1/5) * |(30-30)| + |(30-28)| + |(29-29)| + |(30-31)| + |(30-29)| = 0.8°C

So, on average, the forecast was off by 0.8°C. Not bad, huh?

MAE's Role in Statistics & Probability

MAE is a key metric in regression analysis, a topic you're exploring in your Secondary 4 Math Syllabus. It helps us understand how well our forecast model is performing. A lower MAE means our forecast is more accurate.

What if we could reduce MAE to zero? That would mean our forecast is perfect! In Singaporean high-speed and scholastically intense setting, parents acknowledge that building a solid educational groundwork from the earliest stages can make a major effect in a child's long-term achievements. The journey to the PSLE begins much earlier than the final assessment year, since foundational behaviors and skills in areas including mathematics establish the foundation for higher-level education and analytical skills. With early readiness efforts in the early primary stages, pupils may prevent frequent challenges, build confidence gradually, and form a optimistic mindset towards difficult ideas set to become harder later. math tuition centers in Singapore serves a crucial function within this foundational approach, providing age-appropriate, interactive sessions that introduce fundamental topics like elementary counting, forms, and simple patterns aligned with the Singapore MOE program. These courses utilize enjoyable, engaging techniques to arouse enthusiasm and prevent educational voids from developing, guaranteeing a smoother progression across higher levels. Ultimately, committing in these beginner programs not only alleviates the burden of PSLE and additionally prepares young learners with lifelong thinking tools, giving them a competitive edge in Singapore's meritocratic system.. But alas, that's not possible... or is it?

Stay tuned for our next stop on this journey, where we'll explore the limits of MAE and the future of forecasting in Singapore.

" width="100%" height="480">Metrics for measuring the accuracy of statistical forecasts in Singapore

Mean Absolute Error (MAE)

MAE measures the average magnitude of errors in a set of forecasts without considering their direction. It's useful for Singapore's statistical forecasts as it shows the typical forecast error size.

Root Mean Squared Error (RMSE)

RMSE is the square root of the average of squared forecast errors, giving more weight to larger errors. It's suitable for Singapore's context as it's sensitive to outliers and provides a more conservative estimate.

R-Squared (Coefficient of Determination)

R-Squared indicates the proportion of variance in the dependent variable that is predictable from the independent variable(s). It's relevant for Singapore's forecasts as it helps assess the goodness-of-fit of a model.

Mean Absolute Percentage Error (MAPE)

MAPE measures the average size of forecast errors as a percentage of the actual values. It's useful for Singapore's forecasts as it provides an intuitive measure of forecast accuracy, especially for percentage-based forecasts.

Root Mean Squared Error (RMSE)

RMSE Calculation

To calculate the Root Mean Squared Error (RMSE), we first find the squared difference between the forecasted and actual values, then take the mean of these squared differences, and finally, take the square root of that mean. This process ensures that larger errors are penalized more, giving a more accurate representation of forecast errors. For instance, in Singapore's secondary 4 math syllabus, students might use this formula to calculate the RMSE of forecasted versus actual PSLE scores.

RMSE vs. MAE

RMSE differs from Mean Absolute Error (MAE) in how it handles large errors. While MAE simply takes the average of the absolute differences, RMSE squares the differences first. This makes RMSE more sensitive to outliers and larger errors, which is useful in many real-world scenarios, including Singapore's property market. For example, an overestimation of a property's value by $500,000 would have a much greater impact on the RMSE than the MAE.

As Singaporean educational system places a heavy focus on math proficiency early on, guardians are more and more prioritizing structured assistance to enable their kids navigate the rising complexity of the curriculum in the early primary years. By Primary 2, pupils meet more advanced topics like carrying in addition, basic fractions, and measurement, that build upon basic abilities and set the foundation for sophisticated issue resolution demanded in later exams. Acknowledging the importance of consistent reinforcement to stop early struggles and encourage interest for the subject, many turn to dedicated initiatives in line with MOE guidelines. math tuition singapore delivers targeted , engaging classes developed to make such ideas accessible and enjoyable via hands-on activities, graphic supports, and personalized input from experienced tutors. This strategy not only aids young learners conquer immediate classroom challenges but also cultivates critical thinking and resilience. Over time, these initial efforts contributes to smoother educational advancement, minimizing pressure when learners prepare for key points such as PSLE and establishing a favorable trajectory for ongoing education..

RMSE in Singapore's Property Market

In Singapore's hot property market, developers and investors often use RMSE to measure the accuracy of property price forecasts. For instance, in 2019, the RMSE of forecasted versus actual property price changes was around $30,000, highlighting the challenge of predicting Singapore's property market accurately. This figure is significant, given that the median property price in Singapore is over $1 million.

RMSE in Weather Forecasting

RMSE is also used in weather forecasting, another field that requires accurate predictions. In Singapore, the educational framework culminates primary-level education with a national examination that assesses pupils' academic achievements and decides their secondary school pathways. The test occurs every year for students in their final year of primary education, focusing on key subjects to evaluate comprehensive skills. The Junior College math tuition serves as a standard for placement for fitting secondary courses based on performance. The exam covers subjects like English, Math, Science, and Mother Tongue, featuring structures revised from time to time to match schooling criteria. Grading is based on performance levels spanning 1 through 8, in which the total PSLE Score is the sum of per-subject grades, influencing long-term educational prospects.. The Meteorological Service Singapore (MSS) uses RMSE to evaluate the performance of its numerical weather prediction models. For instance, the RMSE of temperature forecasts in Singapore is typically around 1.5°C, reflecting the challenges of predicting weather patterns in the tropical city-state.

RMSE and Probability

In statistics and probability, which are key components of Singapore's secondary 4 math syllabus, RMSE is used to estimate the standard deviation of a forecast error distribution. This is because the square root of the mean squared error (which is what RMSE calculates) gives an estimate of the standard deviation of the forecast errors. This is a fun fact that students might find interesting, as it shows the connection between RMSE and another key statistical concept.

Mean Absolute Percentage Error (MAPE)

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Forecasting in Numbers: A Tale of MAPE in Singapore

Imagine you're Singapore's Chief Forecaster, tasked with predicting our bustling city-state's future. You're not alone; from predicting GDP growth to anticipating the next HDB flat price surge, forecasts shape our nation's decisions. Today, we dive into the world of Metrics, focusing on the Mean Absolute Percentage Error (MAPE), a forecasting buddy that's been around the block a few times.

MAPE: The Forecaster's Friend

MAPE, my curious friends, is like the honest referee in the forecasting game. It tells us, in simple terms, how far off our predictions are, without getting too technical. The formula? It's just like a simple recipe:

MAPE = (1/n) * ∑|Yi - Fi| / (Yi + Fi) * 100

Where Yi is the actual value and Fi is the forecasted value. Easy peasy, right?

In Singapore's challenging schooling system, the Primary 3 level marks a significant change where students explore further in areas like multiplication facts, fractions, and fundamental statistics, building on earlier foundations in preparation for more advanced critical thinking. Numerous parents observe that classroom pacing on its own may not suffice for all kids, prompting them to seek supplementary help to cultivate interest in math and avoid early misconceptions from developing. During this stage, tailored learning aid is crucial in keeping educational drive and encouraging a development-oriented outlook. best maths tuition centre provides focused, curriculum-aligned guidance using small group classes or individual coaching, emphasizing heuristic approaches and visual aids to demystify challenging concepts. Instructors often integrate playful components and ongoing evaluations to monitor advancement and increase engagement. Finally, this early initiative not only enhances short-term achievements and additionally lays a sturdy groundwork for excelling during upper primary years and the final PSLE exam..

MAPE in Lion City's Forecasting Scene

In Singapore, MAPE has been our trusty sidekick in various forecasts. Remember the 2011 General Election? Pollsters used MAPE to measure how well they predicted the vote shares. Spoiler alert: MAPE was less than 5%, a pretty good score!

Advantages: Why MAPE's a Keeper

  • Easy to understand: MAPE's simple formula makes it a darling among statisticians and laypersons alike.
  • Scale-independent: Whether you're predicting Singapore's next GDP growth or your secondary 4 math class's test scores, MAPE works just fine.

Limitations: MAPE's Not Perfect

  • Sensitive to outliers: A single off-the-charts prediction can throw MAPE's calculation way off.
  • Not defined for zero: MAPE can't handle predictions or actual values of zero. So, no forecasting Singapore's next zero-growth year, okay?

Fun Fact: MAPE's History

MAPE's origins trace back to the 1950s, when American statistician George Box introduced it. But it wasn't until the advent of computers that MAPE truly took off, becoming a staple in forecasting toolkits worldwide.

MAPE & Secondary 4 Math Syllabus, Singapore

You might wonder, where does MAPE fit into our secondary 4 math syllabus, Singapore? Great question! MAPE's a fantastic example of how statistics can be applied in real-life situations, making it a perfect fit for your math classes.

So, the next time you're predicting your class's attendance or Singapore's next economic growth, remember MAPE. It's your trusty forecasting buddy, here to help you measure how close you are to that bullseye!

R-Squared (Coefficient of Determination)

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Unlocking the Power of R-Squared: A Parent's & Student's Guide

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What's the Scoop on R-Squared?

** Imagine you're at a hawker centre, trying to decide between char kway teow and laksa. You ask around, and 80% of the time, you get the same answer: char kway teow is the bomb! Now, if you were to forecast that 80% of the time, you'd enjoy your meal, how accurate would that be? That's where R-squared comes in, lah! **

The R-Squared Formula: Simple as Hokkien Mee

** R-squared, or the coefficient of determination, is a statistical measure that explains how well your forecast (or model) fits the actual data. It's calculated using this simple formula: **

** Don't worry, it's not as scary as it looks. Let's break it down, shall we? - **y_i**: Each data point - **ŷ_i**: Forecasted value for each data point - **mean(y)**: Average of all data points **

R-Squared in Action: Singapore's PSLE Scores

** Let's use Singapore's PSLE scores to see R-squared in action. We'll use the actual scores and our forecast (which is just the mean score). | Student | Actual Score | Forecasted Score | |---|---|---| | John | 225 | 233.5 | | Jane | 240 | 233.5 | | Jim | 210 | 233.5 | | Jane (again) | 245 | 233.5 | **

** So, our forecast explains about 83% of the variation in the PSLE scores. Not too shabby, eh? **

R-Squared: Not Perfect, But Pretty Goodlah!

** R-squared isn't perfect. It can't tell you if your forecast is off by a little or a lot. In Singapore's achievement-oriented schooling system, the Primary 4 stage serves as a key transition during which the program becomes more demanding including concepts like decimal numbers, symmetrical shapes, and elementary algebraic ideas, pushing learners to use logical thinking via systematic approaches. Numerous families recognize that school lessons alone might not fully address personal learning speeds, prompting the search of additional resources to strengthen concepts and spark lasting engagement with maths. As preparation ahead of PSLE builds momentum, regular exercises proves vital in grasping these building blocks without overwhelming developing brains. Singapore exams offers tailored , engaging tutoring aligned with Singapore MOE criteria, including everyday scenarios, puzzles, and technology to transform intangible notions relatable and fun. Experienced educators prioritize detecting weaknesses at an early stage and converting them to advantages through step-by-step guidance. In the long run, this investment fosters tenacity, better grades, and a effortless progression to advanced primary levels, setting students along a route to academic excellence.. But it's a great starting point for understanding how well your forecast matches reality. Here's a quick guide: - **0.9 - 1**: You're practically psychic! - **0.5 - 0.9**: Quite good, but there's room for improvement. - **0 - 0.5**: Not great, but not terrible. There's definitely room for improvement. - **-∞ - 0**: You're better off flipping a coin. **

R-Squared & the Secondary 4 Math Syllabus, Singapore

** If you're studying the secondary 4 math syllabus in Singapore, you'll definitely come across R-squared. It's a key concept in statistics and probability, so make sure you understand it well, lah! **

Fun Fact: The History of R-Squared

** R-squared was first introduced by Sir Francis Galton in the late 1800s. He was a cousin of Charles Darwin and a pioneer in statistics. He used R-squared to measure the accuracy of a weather forecasting model. Pretty neat, huh? **

Interesting Fact: R-Squared in Everyday Life

** R-squared is used everywhere, from weather forecasting to stock market predictions. Even Netflix uses it to recommend shows you might like! So, there you have it! R-squared might seem like a scary statistical measure, but it's really just a way to understand how well our forecasts match reality. Now that you know R-squared, you're ready to tackle the secondary 4 math syllabus, Singapore, and beyond!

Practical Application: Case Study

Real-World Forecasting: A Singaporean Tale

Imagine you're walking down Orchard Road on a weekend, armed with your secondary 4 math skills and a curious mind. You're not just window shopping, you're on a mission to understand Singapore's statistical forecasts. As Primary 5 introduces a elevated layer of intricacy in Singapore's math program, with concepts such as proportions, percentages, angular measurements, and sophisticated problem statements requiring keener critical thinking, parents often search for approaches to guarantee their children remain in front without falling into frequent snares in comprehension. This phase proves essential since it directly bridges to readying for PSLE, where built-up expertise faces thorough assessment, necessitating timely aid crucial for building endurance for addressing step-by-step queries. With the pressure escalating, dedicated assistance helps transform likely irritations into chances for advancement and proficiency. h2 math tuition arms students using effective instruments and personalized coaching aligned to Singapore MOE guidelines, using strategies like model drawing, graphical bars, and practice under time to clarify detailed subjects. Experienced tutors emphasize clear comprehension over rote learning, fostering engaging conversations and mistake review to instill assurance. At year's close, students generally exhibit notable enhancement for assessment preparedness, paving the way for a stress-free transition onto Primary 6 and further in Singapore's competitive academic landscape.. Let's dive into a real-life case study, shall we?

(To be continued with the case study content in the next section)

Engaging Activity: Predict and Evaluate

Activity: The Weather Forecast Challenge

Alright, let's roll up our sleeves and dive into a hands-on activity that'll make learning about forecast accuracy metrics as fun as a Sunday at East Coast Park! Remember, we're drawing from the Secondary 4 Math Syllabus, Singapore by the Ministry of Education, so you know we're keeping it real and relevant.

Objective: By the end of this activity, you'll be able to predict and evaluate forecast accuracy using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), just like a mini meteorologist!

Materials:

  • A weather dataset (we've got one prepared for you, no need to brave the rain!)
  • Calculators
    • In the city-state of Singapore's pressure-filled academic landscape, the Primary 6 year signifies the capstone phase for primary-level learning, during which learners consolidate accumulated knowledge in preparation for the all-important PSLE, facing intensified topics including complex fractions, geometric demonstrations, velocity and ratio challenges, and comprehensive revision strategies. Parents often observe the escalation in complexity can lead to stress or knowledge deficiencies, notably with math, motivating the need for specialized advice to refine abilities and assessment methods. In this pivotal stage, when every mark counts for secondary placement, supplementary programs are vital in specific support and building self-assurance. h2 math online tuition offers in-depth , centered on PSLE sessions that align with the current MOE curriculum, incorporating practice tests, error correction workshops, and adaptive teaching methods to address unique student demands. Proficient instructors emphasize effective time allocation and complex cognitive skills, aiding students handle even the toughest questions smoothly. All in all, such expert assistance doesn't just boosts performance for the forthcoming PSLE while also cultivates focus and a enthusiasm for mathematics that extends through secondary schooling and further..
  • Pencils and paper (for those who love the old-school charm)

Step 1: Gather 'Round the Data Imagine you're huddled around a campfire, but instead of scary stories, we've got a weather dataset. This dataset has historical weather data for Singapore, including temperature and rainfall.

Step 2: Make Your Predictions Now, it's time to channel your inner weather expert! Using the statistical methods you've learned, make predictions for the next seven days' temperatures and rainfall. Don't forget to record your predictions neatly – you'll need them later!

Fun Fact: Did you know that Singapore's highest recorded temperature was 36°C in 1998? Now that's hot, lah!

Step 3: The Big Reveal After making your predictions, it's time to see how accurate the Singapore Meteorological Service was. We'll reveal the actual weather data for the same period. Take a moment to compare your predictions with the actual data – it's like opening a surprise packet!

Step 4: Evaluate, Evaluate, Evaluate Now comes the exciting part – evaluating the forecast accuracy using MAE and RMSE! Here's how you can calculate them:

  • MAE: Sum the absolute differences between your predictions and the actual data, then divide by the number of days. The lower the MAE, the better the forecast!

    MAE = (1/n) * ∑|Actual - Predicted|

  • RMSE: First, find the squared differences between your predictions and the actual data. Then, find the average of these squared differences, and take the square root. The lower the RMSE, the better the forecast!

    RMSE = √[(1/n) * ∑(Actual - Predicted)^2]

Interesting Fact: The term 'forecast' was first used in the 15th century, but weather prediction has been around since ancient times. The Babylonians are believed to be the first to record weather observations around 600 BC!

Step 5: The Results Table Create a table to record your MAE and RMSE values for both temperature and rainfall. This will help you compare your performance and see which metric you're better at predicting.

Step 6: The Grand Finale Compare your results with your classmates. Who's the mini meteorologist of the day? Remember, the goal is to learn and have fun, so don't be too hard on yourself if your predictions weren't spot-on!

History Lesson: Singapore's first weather station was established in 1869 at the Singapore Botanic Gardens. Can you believe that's more than 150 years ago?

So, there you have it – a hands-on, engaging activity that'll help you understand and apply forecast accuracy metrics. Now go forth, young statisticians, and make your mark on the world, one prediction at a time!

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Frequently Asked Questions

MAPE is calculated as the average of the absolute percentage differences between actual and forecast values, divided by the number of forecast periods.
The Theils Inequality Coefficient measures the average relative error between actual and forecast values. Its used to evaluate forecast accuracy by comparing it to perfect forecasts.
RMSE is calculated as the square root of the average of squared differences between actual and forecast values.
MAD is the average of the absolute differences between actual and forecast values. Its a simple measure of forecast error, with no directionality.
R-squared represents the proportion of the variance in actual values thats explained by the forecast values. A higher R-squared indicates a better fit.
DA measures the proportion of forecast periods where the direction of the change (increase or decrease) is correctly predicted.
SMAPE is similar to MAPE, but its more robust when dealing with small actual values. Its calculated as the average of (|A-F| / ((|A| + |F|) / 2)) * 2, where A is the actual value and F is the forecast value.