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:
[tex]y=\alpha +\beta x[/tex]
Here,
Y = dependent variable
X = independent variable
α = intercept
β = slope
The formula to compute the slope and intercept are:
[tex]\alpha =\frac{\sum Y.\sum X^{2}-\sum X\sum XY}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
[tex]\beta=\frac{n.\sum XY-\sum X\sum Y}{n.\sum X^{2}-(\sum X)^{2}}[/tex]
Consider the table below.
Compute the value of α as follows:
[tex]\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[/tex]
Compute the value of β as follows:
[tex]\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[/tex]
The regression equation is:
[tex]y=56.114+5.044\ x[/tex]
For x = 7 compute the value of y as follows:
[tex]y=56.114+5.004\ x\\=56.114+(5.044\times 7)\\=91.422\\\approx 91[/tex]
Thus, the score received by a student who studied 7 hours is 91.
The correct option is (C).
