# Correlation and Regression

11A is a plot and regression analysis question from Norius Chapter 20, concept exercise # 4. I do not have this as a digital copy yet, so if you choose to accept this job, I will scan the problem and email.

11B

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

a. Does there appear to be a linear relationship between the two variables.

b. Would you characterize the relationship as positive or negative?

c. 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.)

d. What's the value for the correlation coefficient?

e. Describe the points that are far from the regression line.

11C

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

a. 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?

b. What is the predicted value for a husband's education if his wife's education is 13 years?

11D

Again, this is from Norius chapter 21, Statistical Concepts exercise 3. I will scan and email the file -- a spss study looking for null and alternative hyotheses and analysis of that.

11E

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

a. Write the linear regression equation to predict father's education from mother's education.

b. 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?

c. What proportion of the variability in mother's education is explained by father's education?

d. How can you tell from the slope if the correlation coefficient between the two variances is positive or negative.

e. 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?

11F

Based on the regression equation developed in question 1, answer the following

a. What do you predict for father's education for a person who has a mother with 12 years of education?

b. What do you predict for average father's education for all people who have a mother with 12 years of education?

Add your analysis at the appropriate spots within the document, then save the file as a .rtf file using the NCU file naming convention and submit for credit.

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#### Solution Summary

The expert examines correlation and regression plots.

Linear Correlation, Regression Lines and Measures of Variation

1) Testing for a Linear Correlation

Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from the table below using a=0.05. Determine whether the is sufficient evidence to support a claim of a linear correlation between the two variables.

Airline Fares Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.05 significance level to test the claim that there is no difference in cost between flights scheduled one day in advance and those scheduled 30 days in advance. What appears to be a wise scheduling strategy?

Flight scheduled 30 days advance 244 260 264 264 278 318 280

Fight scheduled one day in advance 456 614 567 943 628 1088 536

Create scatter plot

2) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

CPI and Subway Fare ; Find the best predicted cost of a slice of pizza when the consumer price index is 182.5 in the year 2000

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.35 1.50 2.00

3) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

Commuters and Parking Space The Metro-North Station of Greenwich, CT has 2804 commuters . Find the best predicted number of parking spots at that station. Is the predicted value close to the actual value of 127?

Commuters 3453 1350 1126 3120 2641 277 579 2532

Parking Spots 1653 676 294 950 1216 179 466 1454

4) Finding Measures of Variation

Find (a) explained variation, (b) unexplained variation,(c) total variation, (d) coefficient of determination,and (e) standard error of estimate Se, In each case, there is sufficient evidence to support a claim of a linear correlation so that it is reasonable to use the regression equation when making predictions

CPI and Subway Fare The consumer price index and the cost of a slice of pizza from table 10-1

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.25 1.75 2.00