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+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 Overall Grades 0 1 1.5 3 4 4.5 5.5 87 86 79 78 76 67 65

Step 1 of 6 :  Find the estimated slope. Round your answer to three decimal places.

Y-intercept

Solution:

 X Y XY X^2 Y^2 0 87 0 0 7569 1 86 86 1 7396 1.5 79 118.5 2.25 6241 3 78 234 9 6084 4 76 304 16 5776 4.5 67 301.5 20.25 4489 5.5 65 357.5 30.25 4225
 n 7 sum(XY) 1401.5 sum(X) 19.5 sum(Y) 538 sum(X^2) 78.75 sum(Y^2) 41780

The slope of the line is denoted by b1 is give by'

Putting the values , we get

b1 = -3.980

Now ,

y intercept denoted by b0 is given by

Putting all values we get

b0 = 87.943

Slope = b1 = -3.980

Y intercept = b0 = 87.943

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