Question

In the following study, researchers wanted to determine if a relationship existed between the minutes of light therapy a patient receives and the patient’s reported score on a seasonal affective disorder (SAD) test.

1. What is ΣX, What is ΣY, What is (ΣX)2, What is (ΣY)2, What is (ΣX2), What is (ΣY2), What is (ΣXY), What is (ΣX)(ΣY), What is N? What is r (round to two decimal places)?

2. What is the slope (b) of the regression line made by this data (round to two decimal places)?

What is the Y intercept (a) of the regression line made by this data (round to two decimal places)?

Given a stress level of 7, what is the predicted SAD test score (round to two decimal places)?

What is the error of participant 6's SAD test score (round to two decimal places)?

3. What is SY (round to two decimal places)? What is the standard error of the estimate (round to two decimal places)?What is the variance in test scores accounted for by variance in stress levels (round to two decimal places)? For this data set, what is the coefficient of alienation?

4. What's the slope of this data (round to two decimal places)? What's the Y intercept (round to two decimal places)?

What's the predicted test score for a stress level of 10 (round to two decimal places)? What's the error of participant 5's score (round to two decimal places)? What's the standard error of the estimate? What is the coefficient of determination?

Participant	Stress Level (X)	Test Score (Y)
1	5	7
2	13	20
3	10	11
4	7	8
5	9	6
6	12	18
7	13	18
8	11	16
9	8	12
10	7	9

Answer 1

1. From the given data

2)

3) Slope b = 1.642 and Intercept = -3.102

4)

Given a stress level of 7,
The predicted SAD test score is y = -3.102 + 1.642(7) = 8.392

Given a stress level of 6,
The predicted SAD test score is y = -3.102 + 1.642(6) = 6.75

5) From the given data

Fitted Regression equation
	X	Y	Y-hat	(Y-Yhat)^2	(Y-Ybar)^2	(Ybar-Ycap)^2
	5	7	5.109489051	3.574031648	30.25	54.61965209
	13	20	18.24817518	3.068890191	56.25	33.04151793
	10	11	13.32116788	5.387820342	2.25	0.674316692
	7	8	8.394160584	0.155362566	20.25	16.85791731
	9	6	11.67883212	32.24913421	42.25	0.674316692
	12	18	16.60583942	1.943683734	30.25	16.85791731
	13	18	18.24817518	0.061590921	30.25	33.04151793
	11	16	14.96350365	1.074324684	12.25	6.068850232
	8	12	10.03649635	3.855346582	0.25	6.068850232
	7	9	8.394160584	0.367041398	12.25	16.85791731
			Total:	51.73722628	236.5	184.7627737

Sum of Squares of error = 51.7372
Mean Sum of square of error = 51.7372 / (n-2) = 51.7372 / (10-2) = 2.5431
i.e. Standard deviation of SSE is 2.5431

Coefficient of determination = 184.76277/236.5 = 0.78124

The coefficient of alienation = sqrt(1 - 0.78124) = 0.4678

6) Given a stress level of 10,
The predicted SAD test score is y = -3.102 + 1.642(10) =13.318

Actual value of Y at X = 10 is 11

Error = 13.318 - 11 = 2.318

Coefficient of determination = 184.76277/236.5 = 0.78124