Answer the questions about the following computer-generated information. Linear

ID: 3318483 • Letter: A

Question

Answer the questions about the following computer-generated information.

Linear correlation coefficient r = 0.794556

Coefficient of determination = 0.631319

Standard error of estimate = 12.9668

Explained variation = 5182.41

Unexplained variation = 3026.49

Total variation = 8208.90

Equation of regression line y’ = 0.725983x + 16.5523

Level of significance = 0.1

Test statistic = 0.794556

Critical value = 0.378419

a. Are both variables moving in the same direction?

b. Which number measures the distances from the prediction line to the actual values?

c. Which number is the slope of the regression line?

d. Which number is the y intercept of the regression line?

e. Which number is the allowable risk of making a type I error?

f. Which number measures the variation explained by the regression?

g. Which measures the scatter of points about the regression line?

h. What is the null hypothesis?

i. Which number is compared to the critical value to see if the null hypothesis should be rejected?

Answer:

a) Yes both the variable are moving in the same direction.

Reason: Since linear correlation coefficient (r) is positive.

b) 12.9668 , standard error of estimate measures the distance from the prediction line to the actual values.

c) 0.725983 is the slope of the regression line. it is the coefficient of x in the regression equation.

d) 16.5523 is the intercept of the regression line.

e) 0.1 , the level of significance is the allowable risk of making type I error.

f) 5182.41 is the measure of explanied variation.

g) 8208.90 , Total variation measures the scatter of points about the regression line.

h) Null Hypothesis : There is no relationship between the two variables. i.e. (r = 0) or (slope = 0)

i) 0.794556 , the test statistic is compared to the critical value to see if the null hypothesis should be rejected.

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