Assignment 11 Problems

Exercise 4 Ch 20

You are a production manager interested in the relationship between defect rate and volume at one of your plants. You’ve taken a random sample of 160 shifts and recorded the percentage of defective items and the volume. Here is the plot of the two variables and the regression statistics:

1. Is there a relationship between defect rate and volume? If so, is it positive or negative/
2. Which variable is the independent variable and which is the dependent variable?
3. Write out the regression equation and sketch it on the plot.
4. What percentage of the variability in the defect rate can be explained by differences in volume?
5. What defect rate would you predict for a shift with a volume of 4000 units?
6. What defect rate would you predict for a shift with a volume of 9000 units?
7. Would you expect all shifts that produced 4000 items to have the same defect rate?
8. What would you estimate the standard deviation of the distribution of the defect rate to be for a volume of 4000 units?
9. If a particular shift produced 4000 items and had a defect rate of 10%, based on the regression model what would be the residual for the shift?

Problem 1 Ch 20

Use the gss.sav data file to answer the following questions;

Problem 1. Using the Graphs menu, make a scatterplot of husband’s education against wife’s education (variables husbeduc and wifeduc ). Edit the chart to draw the regression line and print R².

1. Does there appear to be a linear relationship between the two variables?
2. Would you characterize the relationship as positive or negative?
3. From the plot, estimate the slope and the intercept. (It’s easier to estimate the intercept if you edit the x axis to start at 0.)
4. What’s the value for the correlation coefficient?
5. Describe the points that are far from the regression line.

Graph

Problem 2 Ch 20

From the Regression procedure, obtain the least-squares estimates for the slope and the intercept.

1. Write the regression equation to predict a husband’s education from his wife’s education. What proportion of the variability in husbands’ education can be "explained" by wives’ education?
2. What is the predicted value for a husband’s education if his wife’s education is 13 years?

Regression

Exercise 3 Ch 21

You obtain the following regression statistics for the relationship between defect rate and volume at one of your plants. You have a random sample of results from 160 shifts at the 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 mull hypothesis that there is no linear relationship between the dependent and independent varaibales?
6. Can you reject the null hypothesis that the population correlation coefficient is 0?
7. What would you predict the defeat rate to be on a day when the volume is 4200 units? What would you predict the average defect rate to be for all days with production volumes of 4200?
8. In what way do the two estimates of the defect rate in question 3g differ? (Calculations not required.)

Problem 1 Ch 21

Use the gss.sav date file to answer the following questions:

Problem1. 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 equation 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 base on what you know about the slope? Can you reject the null hypothesis that the population correlation coefficient is 0?

Problem 2 Ch 21

Based on the regression equation developed in problem 1 Ch 21, answer following:

1. What do you predict for father’s education for a person who has a mother with 12 years of education?
2. What do you predict for average father’s education for all people who have a mother with 12 years of education?

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