Question

The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Hours Studying	1	2	3	4	5
Midterm Grades	70	77	84	88	95

1. Find the estimated slope. Round your answer to three decimal places.

2.Find the value of the coefficient of determination. Round your answer to three decimal places.

3.Find the estimated y-intercept. Round your answer to three decimal places

4.Determine the value of the dependent variable of ^y at x=0

5.According to the equation of the regression line, if the independent variable is increased by one unit what is the change in the dependent variable y?

6.Not all points predicted by the linear model fall on the same line True or False

7.Substitute the values found in 1 and 2 in to the equation in the regression line to find the linear model.According to this model, if the value of the independent variable is increased by one unit, then find the dependent variable y.

Answer 1

X	Y	XY	X²	Y²
1	70	70	1	4900
2	77	154	4	5929
3	84	252	9	7056
4	88	352	16	7744
5	95	475	25	9025
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
15	414	1303	55	34654

Sample size, n =	5
x̅ = Ʃx/n = 15/5 =	3
y̅ = Ʃy/n = 414/5 =	82.8
SSxx = Ʃx² - (Ʃx)²/n = 55 - (15)²/5 =	10
SSyy = Ʃy² - (Ʃy)²/n = 34654 - (414)²/5 =	374.8
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 1303 - (15)(414)/5 =	61

1.

Slope, b1 = SSxy/SSxx = 61/10 = 6.1

2.

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = (61)²/(10*374.8) = 0.993

3.

y-intercept, b0 = y̅ -b1* x̅ = 82.8 - (6.1)*3 = 64.5

4.

Predicted value of y at x = 0

ŷ = 64.5 + (6.1) * 0 = 64.5

5.

If the independent variable is increased by one unit, the dependent variable changes by 6.1 units

6. False

7.

Regression equation :

ŷ = 64.5 + (6.1) x