15.6: Linear Regression Exercises
- Page ID
- 18141
Exercise \(\PageIndex{1}\)
How are correlation and regression similar? How are they different?
- Answer
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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
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\(\widehat{y} = \) 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.
Source | \(SS\) | \(df\) | \(MS\) | \(F\) |
---|---|---|---|---|
Model | 34.21 | |||
Error | 31.91 | |||
Total | 66.12 |
- Answer
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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)