Question

The data below are the final exam scores of 10 randomly selected statistics students and the number of hours they studied for the exam. What is the best predicted value for y given x = 7? Assume that the variables x and y have a significant correlation.
Hours, x 3 5 2 8 2 4 4 5 6 3
Scores, y 65 80 60 88 66 78 85 90 90 71
Choose one answer.

A. 89
B. 90
C. 91
D. 92

Answer 1

Answer:

Correct option: (C) 91.

Step-by-step explanation:

To predict the score received by a student if the number of hours studied is 7 can be done using a regression line.

The general form of a regression line is:

$y=\alpha +\beta x$

Here,

Y = dependent variable

X = independent variable

α = intercept

β = slope

The formula to compute the slope and intercept are:

$\alpha =\frac{\sum Y.\sum X^{2}-\sum X\sum XY}{n.\sum X^{2}-(\sum X)^{2}}$

$\beta=\frac{n.\sum XY-\sum X\sum Y}{n.\sum X^{2}-(\sum X)^{2}}$

Consider the table below.

Compute the value of α as follows:

$\alpha =\frac{\sum Y.\sum X^{2}-\sum X\sum XY}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(773\times 208)-(42\times 3406)}{(10\times 208)-(42)^{2}}=56.114$

Compute the value of β as follows:

$\beta=\frac{n.\sum XY-\sum X\sum Y}{n.\sum X^{2}-(\sum X)^{2}}=\frac{(10\times 3406)-(42\times 773)}{(10\times 208)-(42)^{2}}=5.044$

The regression equation is:

$y=56.114+5.044\ x$

For x = 7 compute the value of y as follows:

$y=56.114+5.004\ x\\=56.114+(5.044\times 7)\\=91.422\\\approx 91$

Thus, the score received by a student who studied 7 hours is 91.

The correct option is (C).