15.6: Linear Regression Exercises
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- 22166
How are correlation and regression similar? How are they different?
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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.
What are the parts of the regression line equation? \(\widehat{y} = a + b\text{x}\)
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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
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 |
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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