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	00	0.50.5	1.51.5	22	2.52.5	33	3.53.5
Overall Grades	9696	9595	8888	8585	8484	7676	7575

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.

Step 3 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6: 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 yˆy^ is given by? b0,b1,x,y?

Step 5 of 6: Find the estimated value of y when x=1.5x=1.5. 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.

Answer 1

The following data are passed:

X	Y
0	96
0.5	95
1.5	88
2	85
2.5	84
3	76
3.5	75

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	0	96	0	0	9216
	0.5	95	47.5	0.25	9025
	1.5	88	132	2.25	7744
	2	85	170	4	7225
	2.5	84	210	6.25	7056
	3	76	228	9	5776
	3.5	75	262.5	12.25	5625
Sum =	13	599	1050	34	51667

Based on the above table, the following is calculated:

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

Therefore, based on the above calculations, the regression coefficients (the slope mm, and the y-intercept nn) are obtained as follows:

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Therefore, we find that the regression equation is:

Y = 97.333 - 6.333 X

Step 3 of 6: Determine if the statement "All points predicted by the linear model fall on the same line is

true  

Step 4 of 6: 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^ is given by?

With 1 unit increase in x y will decrease by 6.33 units

Step 5 of 6: Find the estimated value of y when x=1.5 . Round your answer to three decimal places.

Y = 97.333 - 6.333 X

Y = 97.333 - 6.333 *1.5

Y = 97.333 - 9.4995

Y = 87.8335

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

Now, the correlation coefficient is computed using the following expression::

Then, the coefficient of determination, or R-Squared coefficient (R2), is computed by simply squaring the correlation coefficient that was found above. So we get: