Suppose a professor records the number of days absent and the final exam score f

Question

Suppose a professor records the number of days absent and the final exam score for the students in his class. Use this data in the table below to answer questions a through d Click the icon to view a table of critical values for the correlation coefficient. a) Find the least-squares regression line, treating number of absences as the explanatory variable and final exam score as the response variable. cap y = x. + (Round to two decimal places as needed.) (b) Interpret the slope and intercept, if appropriate Choose the best interpretation for the slope. A. The slope indicates the average number of absences. B. The slope indicates the average final exam score. C. The slope indicates the ratio between the average final exam score and the average number of absences. D. The slope indicates the average change in final exam score for an additional absence. E. It is not appropriate to interpret the slope because it is not equal to zero. Choose the best interpretation for the y-intercept. A. The y-intercept indicates the average number of absences for the population. B. The y intercept indicates the average final exam score for the population. C. The y intercept indicates the average final exam score for a student with no absences. D. The y intercept indicates the final exam score of the student with the most absences. E. It is not appropriate to interpret the y intercept because it is outside the scope of the model. Click to select your answer(s).

Explanation / Answer

The regression line of Y on X  is Y = a+ bX, where a and b are obtained by normal equations

Y = n a + b X

XY = aX + b X2

Substituting the values in the above equations, we have

5a + 10b = 387.1

10a+ 30b = 720.7

For solving the above equations, multiply the first equation by 2

10a + 20b = 774.2 ----(1)

10a+ 30b = 720.7---------(2)

(1)-(2) ----> -10b = 53.5

Hence b = -5.35

Substituting the value of b in equation(1), we get a = 88.12

Hence Y = 88.12 - 5.35 X

slope=b= -5.35

Y intercept =a= 88.12

b) Answer: D , Slope indicates average change in final exam score for an additional absence

c) Answer:C. Y intercept indicates Average final exam for a student with no absence

a) X Y X2 XY Y2 0 84.9 0 0 7208.01 1 85 1 85 7225 2 81 4 162 6561 3 71.1 9 213.3 5055.21 4 65.1 16 260.4 4238.01        Sum= 10 387.1 30 720.7 30287.23

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