Question

he 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	11	1.51.5	22	2.52.5	3.53.5	44	5.55.5
Overall Grades	9696	9393	8484	8282	7979	7878	6464

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Find the estimated slope. Round your answer to three decimal places.

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Answer 1

Step 1:

Sum of X = 20
Sum of Y = 576
Mean X = 2.8571
Mean Y = 82.2857
Sum of squares (SS_X) = 14.8571
Sum of products (SP) = -96.7143

Regression Equation = ŷ = b1X + b0

Slope is b1 = SP/SS_X = -96.71/14.86 = -6.510

Step 2: b0 = M_Y - bM_X = 82.29 - (-6.51*2.86) = 100.885

Hence regression equation is

ŷ = -6.510X + 100.885