1. Run a regression equation to predict father’s education from mother’s education (variables paeduc and maeduc). Include 95% confidence intervals for the slope and intercept. Save the standard error of the mean prediction.

1. Write the linear regression to predict father’s education from mother’s education
2. Based on the results of the linear regression can you reject the null hypothesis that there is no linear relationship between father’s and mother’s education.
3. What proportion of the variability in mother’s education is explained by father’s education?
4. How can you tell from the slope if the correlation coefficient between the two variables is positive or negative?
5. What can you conclude about the population correlation coefficient based on what you know about the slope? Can you reject the null hypothesis that the population correlation coefficient is 0?
   2. Use the gss.sav data file to answer the following questions:
   Build a linear regression model to predict a person's education (variable educ ) from the father's (variable paeduc ). Save the Studentized residual, the predicted value, and the change in the coefficients (dfbeta).
   1. Plot the two variables and draw the regression line.
   2. Write the regression equation.
   3. Test the null hypothesis that there is no linear relationship between the two variables.
   4. What proportion of the variability in a person's education is "explained" by their father's education?

3. For the model you developed in question 2, examine the assumptions you need for linear regression.

a. Make a histogram and Q-Q plot of the Studentized residual. What do these suggest about the violation of the normality assumption?

c. Make a scatterplot of the Studentized residual against the predicted education. What should you look for in this plot? What assumption are you checking? Do you suspect that the assumption is not met?

d. Plot the change in slope associated with removing a point against case ID. From the plot, what is the largest change in slope that would occur if you eliminated a point? Use point selection mode to identify the cases with large values for the change in slope. What are their values for the dependent and independent variables?

4. What violations of assumptions, if any, are suggested by the following plots

5. You obtain the following regression statistics for the relationship between defect rate and volume at one of your plants, you have random sample of results from 160 shifts a plant.

1. What are the null and alternative hypotheses
2. What is the population of interest? What is the sample
3. On the basis of the output, what can you conclude about the null hypothesis
4. Can you reject the null hypothesis that the slope is 0
5. Can you reject the null hypothesis that there is no linear relationship between the dependent and the independent variables?
6. Can you reject the null hypothesis that the population correlation coefficient is 0?
7. What would you predict the defect rate to be on the day when the volume is 4200 units? What would you predict the average defect rate to be for all days with production volumes 4200?
8. In what way the two estimates of the defect rate in question 5 g differ( calculation not required).

6. Discuss how to integrate information in this course can be used to test hypotheses. What have you learned about developing a hypothesis? What have you learned are the key issues in the testing of hypotheses? What have you learned in analyzing your data and reporting results?

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