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1. Given the linear correlation...

1. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.

r = 0.75, n = 9 (Points : 5)

Critical values: r = ±0.666, no significant linear correlation

Critical values: r = 0.666, no significant linear correlation

Critical values: r = -0.666, no significant linear correlation

Critical values: r = ±0.666, significant linear correlation

3. Find the value of the linear correlation coefficient r.

x 57 53 59 61 53 56 60

y 156 164 163 177 159 175 151

(Points : 5)

-0.054

0.214

0.109

-0.078

4. Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level alpha.

n = 11, Alpha = 0.01 (Points : 5)

r = 0.765

r = ± 0.602

r = 0.735

r = ± 0.735

5. Use the given data to find the best predicted value of the response variable.

Six pairs of data yield r = 0.789 and the regression equation ŷ=4x-2. Also Ῡ=19.0. What is the best predicted value of y for x = 5? (Points : 5)

22.0

18.0

18.5

19.0

6. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

x 1 3 5 7 9

y 143 116 100 98 90

Choose A, B, C, or D. (Points : 5)

A. ŷ= -150.7+6.8x

B. ŷ= 150.7 - 6.8x

C. ŷ= 140.4 - 6.2x

D. ŷ= -140.4 + 6.2x

8. Use the given information to find the coefficient of determination.

A regression equation is obtained for a collection of paired data. It is found that the total variation is 24.488, the explained variation is 15.405, and the unexplained variation is 9.083. Find the coefficient of determination. (Points : 5)

0.629

0.590

1.590

0.371

9. Use the computer display to answer the question.

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.

The regression equation is

Score = 31.55 + 10.90 Years

Predictor Coef StDev T P

Constant 31.55 6.360 4.96 0.000

Years 10.90 1.744 6.25 0.000

S = 5.651 R-Sq = 83.0% R-Sq (Adj) = 82.7%

Predicted Values

Fit StDev Fit 95.0% CI 95.0% PI

53.35 3.168 (42.72, 63.98) (31.61, 75.09)

(Points : 5)

82.7%

17.0%

91.1%

83.0%

10. Find the explained variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the explained variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

498.103

511.724

87.4757

599.2

11. Find the unexplained variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the unexplained variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

511.724

87.4757

96.103

599.2

12. Find the total variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the total variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

599.2

498.103

511.724

87.4757

13. Find the standard error of estimate for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the the standard error of estimate.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

4.1097

7.1720

5.3999

13.060

14. Construct the indicated prediction interval for an individual y.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.845 + 3.524x and the standard error of estimate is Se = 5.40. Find the 99% prediction interval for the test score of a person who spent 7 hours preparing for the test.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

58 < y < 82

62 < y < 78

35 < y < 104

32 < y < 107

15. Solve the problem.

A confidence interval for the sl

r = 0.75, n = 9 (Points : 5)

Critical values: r = ±0.666, no significant linear correlation

Critical values: r = 0.666, no significant linear correlation

Critical values: r = -0.666, no significant linear correlation

Critical values: r = ±0.666, significant linear correlation

3. Find the value of the linear correlation coefficient r.

x 57 53 59 61 53 56 60

y 156 164 163 177 159 175 151

(Points : 5)

-0.054

0.214

0.109

-0.078

4. Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level alpha.

n = 11, Alpha = 0.01 (Points : 5)

r = 0.765

r = ± 0.602

r = 0.735

r = ± 0.735

5. Use the given data to find the best predicted value of the response variable.

Six pairs of data yield r = 0.789 and the regression equation ŷ=4x-2. Also Ῡ=19.0. What is the best predicted value of y for x = 5? (Points : 5)

22.0

18.0

18.5

19.0

6. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

x 1 3 5 7 9

y 143 116 100 98 90

Choose A, B, C, or D. (Points : 5)

A. ŷ= -150.7+6.8x

B. ŷ= 150.7 - 6.8x

C. ŷ= 140.4 - 6.2x

D. ŷ= -140.4 + 6.2x

8. Use the given information to find the coefficient of determination.

A regression equation is obtained for a collection of paired data. It is found that the total variation is 24.488, the explained variation is 15.405, and the unexplained variation is 9.083. Find the coefficient of determination. (Points : 5)

0.629

0.590

1.590

0.371

9. Use the computer display to answer the question.

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.

The regression equation is

Score = 31.55 + 10.90 Years

Predictor Coef StDev T P

Constant 31.55 6.360 4.96 0.000

Years 10.90 1.744 6.25 0.000

S = 5.651 R-Sq = 83.0% R-Sq (Adj) = 82.7%

Predicted Values

Fit StDev Fit 95.0% CI 95.0% PI

53.35 3.168 (42.72, 63.98) (31.61, 75.09)

(Points : 5)

82.7%

17.0%

91.1%

83.0%

10. Find the explained variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the explained variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

498.103

511.724

87.4757

599.2

11. Find the unexplained variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the unexplained variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

511.724

87.4757

96.103

599.2

12. Find the total variation for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the total variation.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

599.2

498.103

511.724

87.4757

13. Find the standard error of estimate for the paired data.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.8447 + 3.52427x. Find the the standard error of estimate.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

4.1097

7.1720

5.3999

13.060

14. Construct the indicated prediction interval for an individual y.

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is ŷ = 44.845 + 3.524x and the standard error of estimate is Se = 5.40. Find the 99% prediction interval for the test score of a person who spent 7 hours preparing for the test.

x Hours of preparation 5 2 9 6 10

y Test of score 64 48 72 73 80

(Points : 5)

58 < y < 82

62 < y < 78

35 < y < 104

32 < y < 107

15. Solve the problem.

A confidence interval for the sl

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