Question

# 12.4 Study the following Minitab output from a regression analysis to predict y from x. a....

12.4 Study the following Minitab output from a regression analysis to predict y from x.

a. What is the equation of the regression model?
b. What is the meaning of the coefficient of x?
c. What is the result of the test of the slope of the regression model? Let α = .10.Why is the t ratio negative?
d. Comment on r2 and the standard error of the estimate.
e. Comment on the relationship of the F value to the t ratio for x.
f. The correlation coefficient for these two variables is - 0.7918. Is this result surprising to you? Why or why not?

Regression Analysis: Y versus X

The regression equation is
Y = 67.2 - 0.0565 X

 Predictor Coef SE Coef T P 67.231 5.046 13.32 0.000 -0.05650 0.01027 -5.50 0.000 S = 10.32 R-Sq = 62.7% 60.6% 1 3,222.9 3,222.9 30.25 0.000 18 1,918.0 106.6 19 5,141.0

a. The regression equation is: ŷ = enter a number rounded to 1 decimal place * - enter a number rounded to 4 decimal places ** x

b. For every unit of increase in the value of x, the predicted value of y will select an option                                                          decreaseincrease by enter a number rounded to 4 decimal places **.

c. The t ratio for the slope is enter a number rounded to 2 decimal places *** with an associated p-value of .000.
d. r2 is enter a number rounded to 1 decimal place *% of the variability of y is accounted for by x. This is select an option                                                          lowonly a modesthigh proportion of predictability. The standard error of the estimate is enter a number rounded to 2 decimal places ***. This is select an option                                                          bestnot good interpreted in light of the data and the magnitude of the data.

e. The F value which tests the overall predictability of the model is enter a number rounded to 2 decimal places ***. For simple regression analysis, this equals the value of select an option                                                          square of tsquare of Ssquare of r.

f. The select an option                                                          negativepositive is not a surprise because the slope of the regression line is also select an option                                                          negativepositive indicating an select an option                                                          inversedirect relationship between x and y.

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