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	0	1	2	3	5
Midterm Grades	68	69	73	77	85

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 = 34. 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: 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 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

The statistical software output for this problem is:

Hence,

Step - 1: Slope = 3.554

Step - 2: y - Intercept = 66.581

Step - 3: Estimated y value = 3.554*34 + 66.581 = 187.417

Step - 4: Value of dependent variable = bo = 66.581

Step - 5: Change in dependent variable = b1 = 3.554

Step - 6: Coefficient of determination = R - square = 0.978