Question

The table below gives the number of hours ten randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, y = bo + 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. 0.5 2 2.5 Hours Studying 3 3.5 5 5.5 6 60 70 75 79 85 88 91 93 96 100 Midterm Grades Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. 2 Points Keypad Answer(How to Enter)

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: Grades Independent Variable: Hours Grades = 61.905145 + 6.6045016 Hours Sample size: 10 R (correlation coefficient) = 0.97600041 R-sq = 0.95257681 Estimate of error standard deviation: 2.9054984 Parameter estimates: Parameter Estimate Std. Err. Intercept 61.905145 1.9494158 Slope 6.6045016 0.52100327 Alternative DF T-Stat P-value 0 8 31.755743 <0.0001 0 8 12.676507 <0.0001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 1356.5646 1356.5646 160.69383 <0.0001 Error 8 67.53537 8.4419212 Total 9 1424.1 Predicted values: X value Pred. Y 75.114148 s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 1.141461 (72.481934, 77.746362) (67.915553, 82.312743)

Hence,

Step - 1: Slope = 6.605

Step - 2: y - Intercept = 61.905

Step - 3: True

Step - 4: Estimated value = 75.114

Step - 5: b1

Step - 6: Coefficient of determination = 0.953