Question
Heights of Mothers and Daughters The heights (in inches) of a sample of 134 mother> daughter pairs of subjects were measured and the results are
Heights of Mothers and Daughters The heights (in inches) of a sample of 134 mother> daughter pairs of subjects were measured and the results are listed in Data Set 6 "Family Heights" in Appendix B. StatCrunch results are shown below. StatCrunch also indicates that the P-value is less than 0.0001. Is there sufficient evidence to support the claim that there is a linear correlation between the heights of mothers and the heights of their daughters? Explain.
Simple linear regression results: Dependent Variable: FIRST DAUGHTER Independent Variable: MOTHER FIRST DAUGHTER = 42.020798 + 0.35953064 MOTHER Sample size: 134 R (correlation coefficient) = 0.35352441 R-sq = 0.12497951 Estimate of error standard deviation: 2.19515 Parameter estimates:
Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|
Intercept | 42.020798 | 5.3155378 | 0 | 132 | 7.9052769 | <0.0001 |
Slope | 0.35953064 | 0.082801584 | 0 | 132 | 4.3420744 | <0.0001 |
Analysis of variance table for regression model:
Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|
Model | 1 | 90.849583 | 90.849583 | 18.85361 | <0.0001 |
Error | 132 | 636.06624 | 4.8186836 | ||
Total | 133 | 726.91582 |
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