✍️ Free Response Questions (FRQs)
👆 Unit 1 - Exploring One-Variable Data
1.4Representing a Categorical Variable with Graphs
1.5Representing a Quantitative Variable with Graphs
1.6Describing the Distribution of a Quantitative Variable
1.7Summary Statistics for a Quantitative Variable
1.8Graphical Representations of Summary Statistics
1.9Comparing Distributions of a Quantitative Variable
✌️ Unit 2 - Exploring Two-Variable Data
2.0 Unit 2 Overview: Exploring Two-Variable Data
2.1Introducing Statistics: Are Variables Related?
2.2Representing Two Categorical Variables
2.3Statistics for Two Categorical Variables
2.4Representing the Relationship Between Two Quantitative Variables
2.8Least Squares Regression
🔎 Unit 3 - Collecting Data
3.5Introduction to Experimental Design
🎲 Unit 4 - Probability, Random Variables, and Probability Distributions
4.1Introducing Statistics: Random and Non-Random Patterns?
4.7Introduction to Random Variables and Probability Distributions
4.8Mean and Standard Deviation of Random Variables
4.9Combining Random Variables
4.11Parameters for a Binomial Distribution
📊 Unit 5 - Sampling Distributions
5.0Unit 5 Overview: Sampling Distributions
5.1Introducing Statistics: Why Is My Sample Not Like Yours?
5.4Biased and Unbiased Point Estimates
5.6Sampling Distributions for Differences in Sample Proportions
⚖️ Unit 6 - Inference for Categorical Data: Proportions
6.0Unit 6 Overview: Inference for Categorical Data: Proportions
6.1Introducing Statistics: Why Be Normal?
6.2Constructing a Confidence Interval for a Population Proportion
6.3Justifying a Claim Based on a Confidence Interval for a Population Proportion
6.4Setting Up a Test for a Population Proportion
6.6Concluding a Test for a Population Proportion
6.7Potential Errors When Performing Tests
6.8Confidence Intervals for the Difference of Two Proportions
6.9Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
6.10Setting Up a Test for the Difference of Two Population Proportions
😼 Unit 7 - Inference for Qualitative Data: Means
7.1Introducing Statistics: Should I Worry About Error?
7.2Constructing a Confidence Interval for a Population Mean
7.3Justifying a Claim About a Population Mean Based on a Confidence Interval
7.4Setting Up a Test for a Population Mean
7.5Carrying Out a Test for a Population Mean
7.6Confidence Intervals for the Difference of Two Means
7.7Justifying a Claim About the Difference of Two Means Based on a Confidence Interval
7.8Setting Up a Test for the Difference of Two Population Means
7.9Carrying Out a Test for the Difference of Two Population Means
✳️ Unit 8 Inference for Categorical Data: Chi-Square
📈 Unit 9 - Inference for Quantitative Data: Slopes
🧐 Multiple Choice Questions (MCQs)
Is AP Statistics Hard? Is AP Statistics Worth Taking?
Best Quizlet Decks for AP Statistics
⏱️ 2 min read
June 3, 2020
The simplest form of regression is linear regression where we find a linear equation of the form ŷ=a+bx, where a is the y-intercept and b is the slope. Given a scatterplot, there can be infinitely many linear regression approximations, but there is only one best linear regression model, and this is called the least squares regression line (LSRL). We will discuss this and how to find the formula in a couple of sections.
It is also important to note here that our ŷ represents our predicted response variable value, while x represents our explanatory value variable. Since x is given in a data set, it is not necessarily predicted, but our y-value is always predicted from a least squares regression line.
Given a linear regression equation, we can find values of the response variable for values of the explanatory variable not given in the data set. This is more accurate if you stay in the domain of the set of values of the explanatory variable. If you go outside this domain, it is now called extrapolation, and farther outside the domain you go, the less accurate your predictions will be.
image courtesy of: statsforstem.org comfort
In a recent model built using data for 19-24 year olds, a least squares regression line is developed that says that an individual's comfort level with technology (on a scale of 1-10) can be predicted using the least squares regression line: ŷ=0.32x+0.67, where ŷ is the predicted comfort level and x represents one's age.
Predict what the comfort level would be of a 45 year old and why this response does not make sense.
ŷ=15.07 comfort level
This answer does not make sense because we would expect our predicted comfort levels to be between 1 and 10. 15.07 does not make sense. The reason why we have this response is because we were using a data set intended for 19-24 year olds to make inference about a 45 year old. We were extrapolating our data to include someone outside our data set, which is not a good idea. 🙅♂️💡
🎥Watch: AP Stats - Least Squares Regression Lines
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