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, y ˆ = b 0 + b 1 x y^=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 0.5 1.5 1.5 2 2 2.5 2.5 3.5 3.5 4 4 5.5 5.5 Overall Grades 96 96 94 94 90 90 86 86 85 85 80 80 70 70 Table Copy Data 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. According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y ˆ y^ is given by? Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. Determine the value of the dependent variable y ˆ y^ at x=0 x=0 . Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Step 1 of 6: Find the estimated slope =-5.181

. Step 2 of 6: Find the estimated y-intercept. =100.291

step 3:According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y ˆ y^ is given by=b1 =-5.181

step 4:  "Not all points predicted by the linear model fall on the same line" :False

step 5: value of the dependent variable y ˆ y^ at x=0 x=0 is bo =100.291

Step 6 of 6: Find the value of the coefficient of determination =0.961