Skip to main content

# 15.6: Linear Regression Exercises

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Exercise $$\PageIndex{1}$$

How are correlation and regression similar? How are they different?

Answer

Correlation and regression both involve taking two continuous variables and finding a linear relation between them. Correlations find a standardized value describing the direction and magnitude of the relation whereas regression finds the line of best fit and uses it to partition and explain variance.

Exercise $$\PageIndex{2}$$

What are the parts of the regression line equation?  $$\widehat{y} = a + b\text{x}$$

Answer

$$\widehat{y} =$$ The estimated or predicted value of the outcome variable

$$a =$$ The constant or intercept

$$b =$$ The slope of the line

x = A chosen value of the predictor variable

Exercise $$\PageIndex{3}$$

Fill out the rest of the ANOVA Sumary Table below for a linear regression in which N = 55.

Table $$\PageIndex{1}$$- ANOVA Summary Table
Source $$SS$$ $$df$$ $$MS$$ $$F$$
Model 34.21
Error 31.91
Total 66.12
Answer

For this example, the calculated F-score varies a lot based on how many numbers you keep after the decimal point. Math is weird.

Table $$\PageIndex{2}$$- ANOVA Summary Table
Source $$SS$$ $$df$$ $$MS$$ $$F$$
Model 34.21 1 34.21 From 56.82 to about 57.02
Error 31.91 53 0.60 leave blank
Total 66.12 54 leave blank leave blank

## Contributors and Attributions

• Foster et al. (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)

This page titled 15.6: Linear Regression Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Michelle Oja.

• Was this article helpful?