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, y^=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	0	1	2	5	6
Midterm Grades	64	65	81	89	94

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:

Determine the value of the dependent variable yˆ at x=0.

Step 4 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ

Step 5 of 6:

Find the estimated value of y when x=1x=1. 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

Ans:

	hours of studying,x	midterm grades,y	xy	x^2	y^2
1	0	64	0	0	4096
2	1	65	65	1	4225
3	2	81	162	4	6561
4	5	89	445	25	7921
5	6	94	564	36	8836
Total	14	393	1236	66	31639

1)slope,b=(5*1236-14*393)/(5*66-14^2)=5.060

2)y-intercept=(393-5.0597*14)/5=64.433

3)the value of the dependent variable yˆ at x=0 is=intercept=64.433

4)

Regression equation:

y'=64.433+5.060 x

When the value of the independent variable is increased by one unit, then the change in the dependent variable yˆ

=5.060

5)when x=1

y'=64.433+5.060*1

y'=69.493

6)correlation coefficient,r=(5*1236-14*393)/SQRT((5*66-14^2)*(5*31639-393^2))=0.957

The coefficient of determination,R^2=0.957^2=0.916