# Linear Correlation, Critical Value, and Regression Equations

Find the value of the linear correlation coefficient r, the critical value, and determine whether there is a linear correlation.

1) The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands):

(see attached file for data)

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Estimate the current GPA for a student whose entering GPA is 3.6.

2) Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs.

(see attached file for data)

Find the best predicted value of y corresponding to the given value of x.

3) The regression equation relating attitude rating (x) and job performance rating (y) for the employees of a company is Ten pairs of data were used to obtain the equation. The same data yield and What is the best predicted job performance rating for a person whose attitude rating is 73?

(see attached file for solution)

Use the computer display to answer the question.

4) A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score.

(see attached file for data)

Use the software results above to determine what percentage of the total variation in test scores can be explained by the linear relationship between years of study and test scores?

Perform the indicated goodness-of-fit test.

5) A company manager wishes to test a union leader's claim that absences occur on the different week days with the same frequencies. Test this claim at the 0.05 level of significance if the following sample data have been compiled.

(see attached file for data)

Use a test to test the claim that in the given contingency table, the row variable and the column variable are independent.

6) Tests for adverse reactions to a new drug yielded the results given in the table. At the 0.05 significance level, test the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced).

(see attached file for data)

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#### Solution Summary

This solution is comprised of a detailed explanation for correlation coefficient, regression analysis and chi-square test. Correlation coefficient is tested with t test and regression equation is calculated using excel to answer the questions by showing all the formulas and calculations. Full interpretation is given for correlation and regression analysis and also the chi-square test is applied with the help of excel to answer the questions related to categorical analysis.

Statistics: Pearson Correlation, Regression Equation

See attached file for tables.

Problem Set 1: Chapter 16, problems 2, 6c, 14; Chapter 17, problem 14

2. What information is provided by the numerical value of the Pearson correlation?

6. For the following scores,

X Y

1 5

2 9

4 3

5 1

3 2

c. Compute a Pearson Correlation

14. It is well known that similarity. Compute a Pearson correlation for these data and determine whether there is a significant correlation between attitudes for husbands and wives. Set alpha at .05, two-tailed.

Couple Wife (X) Husband (Y)

A 11 14

B 6 7

C 16 15

D 4 7

E 1 3

F 10 9

G 5 9

H 3 8

Chapter 17

14. Problem 15 in Chapter 16 described a study examining the effectiveness of a 7-minute Screen test for Alzheimer's disease: A sample of n = 9, mean scores on the 7-minute test = M = 7, SS = 92. The cognitive test scores averaged M = 17 with SS = 236. For these data, SP = 127.

a. Find the regression equation for predicting the cognitive scores from the 7-Minute Screen score.

b. What percentage of variance in the cognitive scores is accounted for by the regression equation?

c. Does the regression equation account for a significant portion of the variance in the cognitive scores? Use Ã?¯Ã??Ã?¡ = .05 to evaluate the F-ratio.