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, yˆ=b0+b1x, 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             2             2.5         3             4             6

Overall Grades 98          93        91           82           75         64          63

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 : 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 5 of 6 : Determine the value of the dependent variable yˆ at x=0.

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 = -7.085

Step - 2: Intercept = 100.089

Step - 3: Estimated value = -7.085*34 + 100.089 = -140.801

Step - 4: b1

Step - 5: Value of dependent variable = 100.089

Step - 6: Coefficient of determination = 0.888