Question

the data below represent the number of absences, x, and the final grade, y, for a sample of college students at a large university. complete parts (a) through (e) below.
no. of absences, x final grade, y
0 87.9
1 85.1
2 82.2
3 79.8
4 76.9
5 72.5
6 63.0
7 67.6
8 64.8
9 61.9
y = □x + □
(round to three decimal places as needed.)
(b) interpret the slope and y - intercept, if appropriate.
interpret the slope. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(round to three decimal places as needed.)
a. for every unit change in the final grade, the number of days absent falls by □ days, on average.
b. for zero days absent, the final score is predicted to be □.
c. for a final score of zero, the number of days absent is predicted to be □ days.
d. for every day absent, the final grade falls by □, on average.
e. it is not appropriate to interpret the slope.
interpret the y - intercept. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(round to three decimal places as needed.)
a. for zero days absent, the final score is predicted to be □.
b. for a final score of zero, the number of days absent is predicted to be □ days.
c. for every unit change in the final grade, the number of days absent falls by □ days, on average.
d. for every day absent, the final grade falls by □, on average.
e. it is not appropriate to interpret the y - intercept.

Explanation:

Step1: Calculate the slope

Use the formula for the slope \(m=\frac{n\sum(xy)-\sum x\sum y}{n\sum(x^{2})-(\sum x)^{2}}\).
First, calculate \(\sum x = 0 + 1+2 + 3+4+5+6+7+8+9=45\), \(\sum y=87.9 + 85.1+82.2+79.8+76.9+72.5+63.0+67.6+64.8+61.9 = 701.7\), \(\sum(xy)=0\times87.9+1\times85.1 + 2\times82.2+3\times79.8+4\times76.9+5\times72.5+6\times63.0+7\times67.6+8\times64.8+9\times61.9=0 + 85.1+164.4+239.4+307.6+362.5+378+473.2+518.4+557.1 = 3085.7\), \(\sum(x^{2})=0^{2}+1^{2}+2^{2}+3^{2}+4^{2}+5^{2}+6^{2}+7^{2}+8^{2}+9^{2}=0 + 1+4+9+16+25+36+49+64+81 = 285\), \(n = 10\).

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Step2: Calculate the y - intercept

Use the formula \(b=\frac{\sum y-m\sum x}{n}\).

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So the regression equation is \(y=-2.70x + 82.32\)

Step3: Interpret the slope

The slope \(m=-2.70\). For every day absent (\(x\) increases by 1), the final grade (\(y\)) falls by \(2.70\) on average.

Step4: Interpret the y - intercept

The y - intercept \(b = 82.32\). For zero days absent (\(x = 0\)), the final score is predicted to be \(82.32\)

Answer:

(a) The regression equation is \(y=-2.70x + 82.32\)

(b)

• Slope: C. For every day absent, the final grade falls by \(2.70\), on average.
• y - intercept: A. For zero days absent, the final score is predicted to be \(82.32\)