Question

9. 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 62 66 76 77 81

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Find the estimated value of y when x=2. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable yˆ at x=0.

Step 5 of 6: Find the error prediction when x=2. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Independent variable (X): Hours studying

Dependent variable (Y): Midterm grades

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	1	62	1	3844	62
	2	66	4	4356	132
	3	76	9	5776	228
	4	77	16	5929	308
	5	81	25	6561	405
Total	15	362	55	26466	1135

Step 1:

Answer: 4.900

Step 2:

Answer: 57.700

Step 3:

Answer: 67.500

Step 4:

Answer: 57.700

Step 5:

The actual value for X=2 is 66 so the error prediction when x=2 is

residual = actual - predicted = 66 - 57.7 = 8.3

Answer: 8.3

Step 6:

Answer: 0.933