Math 137 Module 12 Review Homework
Daughter and mother height LAMC students Spring 2016
Simple linear regression results:
Dependent Variable: daughter's height
Independent Variable: mother's height
daughter's height = 3.5775438 + 0.97379782 mother's height
Sample size: 25
R (correlation coefficient) = 0.94821641
R-sq = 0.89911437
Estimate of error standard deviation: 4.0885799
Parameter estimates:
Intercept / 3.5775438 / 4.0740938 / ≠ 0 / 23 / 0.87812014 / 0.389
Slope / 0.97379782 / 0.068016154 / ≠ 0 / 23 / 14.317155 / <0.0001
1. Describe the association between a mother’s and daughter’s height.
There is a strong positive linear association between the mother’s height and daughter’s height. OR
As the mother’s height increases, the daughter’s height also increases.
2. Use the regression line equation (if applicable) to predict a daughter’s height if the mother’s height is 59 inches.
61.0 inches
3. Use the regression line equation (if applicable) to predict a daughter’s height if the mother’s height is 88 inches.
Cannot extrapolate. (Beyond the scope of the data.)
4. What is the slope of the regression line? What does the slope mean in this context? (Hint: No need to compute.)0.97379782or about 0.97
For each additional inch in the mother’s height, the daughter’s height increases by about 0.97 inches.
5. What is the y-intercept of the regression line? What does the y-intercept mean in this context? (No need to compute). Does it have meaning in this case?3.5775438or about 3.6
When the mother’s height is zero inches, the daughter’s height will be 3.6 inches which in this case has no meaning.
The following statistics for this scatterplot were found to be:
6. Given the scatterplot and these statistics, how well does the regression line fit this data? How confident could one be in making predictions with the regression line? (Use the value of r to support your answer.)
Since the correlation is strong (0.948) and the percent of explained variation is high (89.9%) one can be confident in using this model to make predictions. Further, one would check the standard error which is 4.0885799 inches in this case. So when making predictions on the daughter’s height, one can expect an error of about ±4.1 inches which is considerable. Based on the standard error, I would not be confident in using this model to make predictions on the daughter’s height based on the mother’s height.
7. Explain the meaning in context of with respect to this problem.89.9% of the total variation in the daughter’s height can be explained by the mother’s height. (The other 10.1% of the variation is due to other factors.)
8. Are there any outliers? If so, state the ordered pairs that are outliers.All points seem to follow the linear pattern. Therefore there are no outliers.