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+b1xy^=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	4	5	5.5
Overall Grades	94	87	82	79	70	67	60

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: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6: Find the estimated value of y when x = 60. Round your answer to three decimal places.

Step 5 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 ˆy.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

show how to do in minitab if possible.

Answer 1

step 1: estimated slope = -6.075

Step 2 : y intercept =94.792

step 3: false

step 4:

predicted value =94.792+60*-6.075=

-269.708

step 5:

if the value of the independent variable is increased by one unit, then find the change in the dependent variable ˆy =b1 =-6075

step 6:

SST=Syy=		856.0000
SSE =Syy-(Sxy)2/Sxx=		17.5849
SSR =(Sxy)2/Sxx =		838.4151

Coeffficient of determination R^2 =SSR/SST=

0.979