15.6: Linear Regression Exercises

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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)
Dr. MO (Taft College)