# Correlation and Regression

Applicants for a particular job that involves extensive travel in Spanish speaking countries, must take a proficiency test in Spanish. The sample data below was obtained in a study of the relationship between the numbers of years applicants have studies Spanish and their score on the test.

# of Years (χ) 3 4 4 2 5 3 4 5 3 2

Score 57 78 72 58 89 63 73 84 75 48

Partial Minitab output is provided below.

Mintab----Regression Analysis

The regression equation is score = 31.5 + 10.9*years

S = 5.651 R -SQ = 83.0% R-Sq (adj) = 80.9%

Analysis of Variance

Source DF SS MS F

P

Regression 1 1248.6 1248.6 39.09

0.000

Residual Error 8 255.5 31.9

Total 9 1504.1

a. What is the correlation coefficient, r?

b. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not zero and hence that the number of years of study is useful as a predictor of score on the test? Explain.

c. do the data provide sufficient evidence to conclude that the number of years of study and test score are linearly positively correlated: Use α = 0.01.

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#### Solution Preview

see attached file where formatting is conserved

a. What is the correlation coefficient, r?

Correlation coefficient= square root of R -SQ= square root of .83= 0.91

b. At the 5% level of significance, do the data provide sufficient evidence to conclude that the slope of the population regression line is not zero and hence that the number of years of study is useful as a predictor of score on the test? Explain.

To determine this we need to calculate standard error of regression coefficient= Sb

Standard error of regression coefficient= Sb=S/square root of {summation of (X2)-n*(Mean X)^2}

standard error of estimate S = 5.651 ...

#### Solution Summary

Minitab output is used to interpret correlation and regression coefficients in a study of the relationship between the numbers of years applicants have studies Spanish and their score on the proficiency test in Spanish.