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15.6: Linear Regression Exercises

  • Page ID
    22166
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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

    15.6: Linear Regression Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michelle Oja.

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