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

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

Y-intercept

Answer 1

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)	1401.50
sum(X)	19.50
sum(Y)	538.00
sum(X^2)	78.75
sum(Y^2)	41780.00

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