Question

# The table below gives the number of hours spent unsupervised each day as well as the...

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 1.5 2.5 3 4.5 5 6 Overall Grades 94 92 86 82 79 71 62

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=2.5. Round your answer to three decimal places.

Step 4 of 6: Determine the value of the dependent variable yˆ at x=0 (b0, b1, x, y)

Step 5 of 6: Find the error prediction when x=2.5. Round your answer to three decimal places.

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

Ans:

 1 2 3 4 5 6 7 Total Hours Unsupervised,x 0 1.5 2.5 3 4.5 5 6 22.5 Overall Grades,y 94 92 86 82 79 71 62 566 xy 0 138 215 246 355.5 355 372 1681.5 x^2 0 2.25 6.25 9 20.25 25 36 98.75 y^2 8836 8464 7396 6724 6241 5041 3844 46546

1)

slope,b1=(7*1681.5-22.5*566)/(7*98.75-22.5^2)=-5.214

2)

intercept,b0=(566-(-5.21351)*22.5)/7=97.615

3)

Regression equation:

y'=97.615-5.214 x

when x=2.5

y'=97.615-5.214*2.5=84.580

4)

when x=0

y'=97.615-5.214*0

y'=97.615

5)

observed value of y when x=2.5 is 86

Error=86-84.580=1.420

6)

r=(7*1681.5-22.5*566)/SQRT((7*98.75-22.5^2)*(7*46546-566^2))=-0.9159

coefficient of determination,R^2=(-0.9159)^2=0.920

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