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		1.20		−0.055	8		2.22		0.028
2		1.87		−0.040	9		2.60		0.030
3		1.04		−0.029	10		2.77		0.033
4		2.54		−0.018	11		2.77		0.064
5		2.19		−0.018	12		3.31		0.077
6		2.63		0.018	13		3.65		0.124
7		1.99		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 +

Make a scatterplot with this line drawn on it.

(b) On your plot, show the "up and over" lines that predict brain activity for social distress score 2.6. 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

The regression equation is defined as,

Where, predictor variable Y is brain activity and response variable X is social distress

The least square estimate of intercept and slope are,

Subject	Social distress, X	Brain activity, Y	X^2	Y^2	X*Y
1	1.2	-0.055	1.44	0.003025	-0.066
2	1.87	-0.04	3.4969	0.0016	-0.0748
3	1.04	-0.029	1.0816	0.000841	-0.03016
4	2.54	-0.018	6.4516	0.000324	-0.04572
5	2.19	-0.018	4.7961	0.000324	-0.03942
6	2.63	0.018	6.9169	0.000324	0.04734
7	1.99	0.021	3.9601	0.000441	0.04179
8	2.22	0.028	4.9284	0.000784	0.06216
9	2.6	0.028	6.76	0.000784	0.0728
10	2.77	0.028	7.6729	0.000784	0.07756
11	2.77	0.028	7.6729	0.000784	0.07756
12	3.31	0.028	10.9561	0.000784	0.09268
13	3.65	0.028	13.3225	0.000784	0.1022
SUM	30.78	0.047	79.456	0.011583	0.31799

Form the data values, the values are calculated as,

The regression equation is,

The scatter plot is obtained in excel. The screenshot is shown below,

For social distress score = 2.6,

c)

The R square value is obtained using the formula,

Hence the percent of variation explained by model is 56.91%