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.

X: Hours Studying 0 1 4 5 6

Y: Midterm Grades 69 71 79 90 99 Table

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=4. Round your answer to three decimal places.

Step 4 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6: Find the error prediction when x=4. 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

The statistical software output for this problem is :

Step - 1) Slope = 4.679

Step - 2) Y-intercept = 66.627

Step - 3) estimated value = 85.343

Step - 4) true

Step - 5)  error prediction = 79 - 85.343 = -6.343

Step - 6) the coefficient of determination = 0.901