Question

The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=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	11	22	33	3.53.5	44	4.54.5	55
Midterm Grades	6868	7272	7373	7575	7676	9191	9494 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Find the estimated y-intercept. Round your answer to three decimal places. Determine the value of the dependent variable yˆy^ at x=0x=0. Find the estimated value of y when x=5x=5. Round your answer to three decimal places. Find the error prediction when x=5x=5. Round your answer to three decimal places. 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:

Simple linear regression results: Dependent Variable: Grades Independent Variable: Hours Grades 58.2814376.1317365 Hours Sample size: 7 R (correlation coefficient) 0.86622534 R-sq 0.75034634 Estimate of error standard deviation: 5.4629947 Parameter estimates: Std. Err. Alternative DF P-value Parameter Estimate T-Stat 05 10.421703 0.0001 Intercept 58.281437 5.5923143 05 3.8765637 0.0117 Slope 6.1317365 1.5817453 Analysis of variance table for regression model: F-stat P-value Source DF SS MS Model 1 448.49273 448.49273 15.027746 0.0117 5 149.22156 29.844311 Error Total 6 597.71429 Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 88.94012 (80.17898, 97.70126) (72.388216, 105.49202) 5 3.4082326 Ln

Hence,

Step - 1: Slope = 6.132

Step - 2: y - Intercept = 58.281

Step - 3: Value of dependent variable = bo = 58.281

Step - 4: Estimated value = 88.940

Step - 5: Error prediction = 94 - 88.940 = 5.06

Step - 6: Coefficient of determination = 0.750