he data below represent the number of days absent, x, and the final grade, y, fo

Question

he data below represent the number of days absent, x, and the final grade, y, for a sample of college students at a large university Complete parts (a) through (e) low o. of absences, x 0 1 2 3 4 56 78 9 inal grade, y 884 855 825 799 76.9 725 628 673 644 614 Find the least-squares regression line treating the number of absences, x, as the explanatory variable and the final grade, y, as the response variable ound to three decimal places as needed) )Interpret the slope and y-intercept, if appropriate terpret the slope Select the correct choice below and, if necessary, fill in the answer box to complete your choice lound to three decimal places as needed) A. For zero days absent, the final score is predicted to be B. Eons dau she ont the final ararda falle sran ck to select your answer(s) ave for Later

Explanation / Answer

Given data is as follows-

Let us look at the regression output now-

a)

Least Square Regression line:

Y(Final Grade) = 88.4 - 3.16*X

b)

Intercept is 88.4

Slope is -3.16

a: For zero days absent, Grade is nothing but the intercept which is 88.4

b: Grade falls on an average by 3.16 for every day of absence, which is the slope

c: X = 88.4/3.16 = 28 days of absence

d: We can take values of Grades to be 88 and 87

For 88, No. of days absent is 3.16X = 0.4, X=0.4/3.16

For 87, X= 1.4/3.16

So, we cannot really come up with the average difference as it changes from value to value

e: No, we can interpret slope like we did in part-(b)

c)

For X=5, Y = 88.4-3.16*5= 72.6

Predicted : 72.6

Observed :72.5

Residual is 0.1

So, predicted value is 0.1 above the actual value

d)

As absents increase, grades decrease

So, that would be (B)

e)

This will be (A)

We can predict the value but that exceeds the scope of the model

Let me know if you need anything else, if not please don't forget to like the answer :)

x- No. of absent days y- Final Grade 0 88.4 1 85.5 2 82.5 3 79.9 4 76.9 5 72.5 6 62.8 7 67.3 8 64.4 9 61.4

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