Question 3: Calculate the linear regression of strength on height. Report the regression equation to a suitable number of decimal places. How does the result of the significance test of the slope of this line differ from the test for the correlation of strength and height?
Click Analyze, Regression, Linear. Select Quadriceps strength into Dependent and Height into Independent. Make sure that Method is Enter. Click OK.
You should get the following output:
Variables Entered/Removed^{b} | |||
---|---|---|---|
Model | Variables Entered | Variables Removed | Method |
1 | Height (cm)^{a} | Enter | |
a All requested variables entered. | |||
b Dependent Variable: Quadriceps strength (newtons) |
Model Summary | ||||
---|---|---|---|---|
Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
1 | .419^{a} | .176 | .155 | 103.13469 |
a Predictors: (Constant), Height (cm) |
ANOVA^{b} | ||||||
---|---|---|---|---|---|---|
Model | Sum of Squares | df | Mean Square | F | Sig. | |
1 | Regression | 88510.562 | 1 | 88510.562 | 8.321 | .006^{a} |
Residual | 414833.829 | 39 | 10636.765 | |||
Total | 503344.390 | 40 | ||||
a Predictors: (Constant), Height (cm) | ||||||
b Dependent Variable: Quadriceps strength (newtons) |
Coefficients^{a} | ||||||
---|---|---|---|---|---|---|
Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | ||
B | Std. Error | Beta | ||||
1 | (Constant) | -907.626 | 426.612 | -2.128 | .040 | |
Height (cm) | 7.203 | 2.497 | .419 | 2.885 | .006 | |
a Dependent Variable: Quadriceps strength (newtons) |
Hence the regression equation is:
quadriceps strength (N) = −908 + 7.20 × height (cm).
We do not need to report the coefficients to the same number of decimal places. I have given both to three significant figures.
The test of significance for the test of the regression slope = 0 in the population gives P = 0.006, which is identical to the test of the correlation coefficient = 0 in the population. These tests always give identical P values.
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