Question

The table below gives data from a study that shows that social exclusion causes "real pain." That is, activity in the area of the brain that responds to physical pain goes up as distress from social exclusion goes up. The scatterplot for this data shows a moderately strong linear relationship. The data are given below.

		Social		Brain			Social		Brain
Subject		distress		activity	Subject		distress		activity
1		1.22		−0.055	8		2.18		0.027
2		1.85		−0.040	9		2.58		0.029
3		1.02		−0.028	10		2.73		0.033
4		2.52		−0.019	11		2.73		0.064
5		2.13		−0.019	12		3.39		0.077
6		2.65		0.019	13		3.61		0.124
7		2.01		0.021

(a) What is the equation of the least-squares regression line for predicting brain activity from social distress score? (Round your answers to four decimal places.)

brain activity

= _______   social distress + _______

(b) On your plot, show the "up and over" lines that predict brain activity for social distress score 2.3. Use the equation of the regression line to get the predicted brain activity level. Verify that it agrees with your plot. (Round your answer to four decimal places.)
  _________

(c) What percent of the variation in brain activity among these subjects is explained by the straight-line relationship with social distress score? (Round your answer to a whole number.)
_________ %

Answer 1

	Distress	Activity	D^2	A2	D*A
	1.22	-0.055	1.4884	0.003025	-0.0671
	1.85	-0.04	3.4225	0.0016	-0.074
	1.02	-0.028	1.0404	0.000784	-0.02856
	2.52	-0.019	6.3504	0.000361	-0.04788
	2.13	-0.019	4.5369	0.000361	-0.04047
	2.65	0.019	7.0225	0.000361	0.05035
	2.01	0.021	4.0401	0.000441	0.04221
	2.18	0.027	4.7524	0.000729	0.05886
	2.58	0.029	6.6564	0.000841	0.07482
	2.73	0.033	7.4529	0.001089	0.09009
	2.73	0.064	7.4529	0.004096	0.17472
	3.39	0.077	11.4921	0.005929	0.26103
	3.61	0.124	13.0321	0.015376	0.44764
Sum	30.62	0.233	78.74	0.034993	0.94171
Mean	2.355385	0.017923
N	13	13

Y'=a+bX

b) X= 2.3

c) Percentage of variation explained:(Coefficient of determination or R-squared value)

Correlation coefficient:

The coefficient of determination:

Percent of the variation in brain activity among these subjects is explained by the straight= 0.756923*100 = 75.6923%