Question

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line. Ĵ = bo+byx, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. 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 Unsupervised 0.5 1.5 2 3.5 4 4.5 5.5 Overall Grades 94 82 77 74 73 61 60 Table < Copy Data > Prev Nex Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Answer How to Enter) 2 Points 1 Tables Keypad Keyboard Shortcuts

Answer 1

The statistical software output for this problem is :

Simple linear regression results: Dependent Variable: y Independent Variable: x y=93.724907 - 6.2825279x Sample size: 7 R (correlation coefficient) = -0.95147764 R-sq=0.9053097 Estimate of error standard deviation: 3.9830496 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 93.724907 3.1710403 +0 5 29.556517 <0.0001 Slope -6.2825279 0.90866456 +05 -6.9140232 0.001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 758.39087 758.39087 47.803717 0.001 Error 5 79.32342 15.864684 Total 6 837.71429 Predicted values: X value Pred. Y s.e.(Pred. y) 95% C.I. for mean 95% P.I. for new 4.5 65.453532 1.9878196 (60.343679, 70.563384) (54.010513, 76.896551)

Step - 1) Slope = -6.283

Step - 2) Y-intercept = 93.725

Step - 3) b0

Step - 4) false

Step - 5)  Estimated value = 65.454

Step - 6) the coefficient of determination = 0.905