2. The following table represents data on the number of homework assignments com

Question

2. The following table represents data on the number of homework assignments completed, X, versus grade, Y, on a t q uiz. Note all frequencies f Quiz Grade 12 16 HW Y2 0 2 2 4 17 16 6 Totals a. Find the means and standard deviations of X and Y. (Use n, not n - 1.) b. Find and interpret the correlation[You can do (b) and (c) in either order.] c. Find the regression coefficients aand b, and then the equation of the regression line What grade does that line predict for a student who finished three HW assignments? How many HW assignments would lead us to predict a grade of 19? What change in test grade would be predicted if the number of HW assignments increases by 3? How much of the variation in test grade is predicted by the number of HW assignments completed? (1) What is the explained error in using y in place of y, for the student who finished 4 homework assignments? (2) What is the residual error for a student who finished 5homework assignments and got a quiz grade of 17? d. e. f. g. h. i. Is it reasonable to use the regression line we found to predict the grade for someone who finished atotalof 8 assignments? Why or why not?

Explanation / Answer

a.

Descriptive Statistics: HW X, Quize Grade Y

Total
Variable Count Mean StDev
HW X 7 3.429 2.149
Quize Grade Y 7 14.29 3.77

b.

Correlations: HW X, Quize Grade Y

Pearson correlation of HW X and Quize Grade Y = 0.619

Threre is positive correlation between HW X and Quize Grade Y

c.

Regression Analysis: Quize Grade Y versus HW X

The regression equation is
Quize Grade Y = 10.6 + 1.09 HW X

d. HWX=3

Quize Grade Y = 10.6 + 1.09 *3=13.87

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