Question

Researchers measured the amount of gray matter in the brains of 35 individuals. Gray matter is a major component of the nervous system, involved in many processes including muscle control, sensory perception, emotions, and decision making. In order to determine the link between intelligence and social circle size, they then recorded the number of Facebook friend each subject had. The scatterplot below shows the relationship between these two variables along with the least squares fit. Round all calculated results to 4 decimal places.

1.The relationship between measure of gray matter and number of Facebook friends is  ? positive negative ,  ? weak strong , and  ? linear non-linear .

2. The explanatory variable is  ? measure of gray matter brain size number of Facebook friends sociality  and the response variable is  ? measure of gray matter brain size number of Facebook friends sociality .

The summary statistics for number of Facebook friends and measure of gray matter are listed below. The correlation between number of Facebook friends and measure of gray matter is 0.3567 .

Measure of gray matter: mean = -0.1086, standard deviation = 0.9363

Number of Facebook friends: mean = 357.7714, standard deviation = 176.5170

3. The equation for the regression line is y =  +  x

4.Complete the following sentence to interpret the slope of the regression line:

An increase of 0.5 in measure of gray matter corresponds to a/an  ? decrease increase  of  in number of Facebook friends.

5. The recorded measure of gray matter for Subject A is 0.1. Use the regression equation to estimate the number of Facebook friends for this individual.

6. The number of Facebook friends for Subject A is 260. Complete the following sentence:

The residual for Subject A is  . This means the number of Facebook friends for Subject A is
A. the same as
B. lower than
C. higher than
the number of Facebook friends predicted by the regression model.

7. Another individual (not included in this data set) has a measure of gray matter of 2.5. Would it be appropriate to use this linear model to predict the number of Facebook friends for this individual?

A. Yes, because 2.5 is a reasonable measure of gray matter for humans.
B. No, because 2.5 is beyond the range of the data used to build the regression model.
C. No, because 533.1788 number of Facebook friends is too large to be a reasonable number of Facebook friends, even for this point.

8. What are the conclusions of this study? Choose all that apply.

A. Measures of gray matter do not correlate to counts of Facebook friends
B. Increasing the measure of gray matter an individual has will increase the number of Facebook friends they have.
C. Measures of gray matter correlate to counts of Facebook friends
D. Increasing the number of Facebook friends an individual has will increase the measure of gray matter they have.
E. Large measures of gray matter cause individuals to have larger counts of Facebook friends
F. Large measures of gray matter cause individuals to have smaller counts of Facebook friends

Answer 1

1)

The relationship between measure of gray matter and number of Facebook friends is positive weak and linear

2)

The explanatory variable is measure of gray matter  and the response variable is   number of Facebook friends

3)

	n=		20
	x̅ =		-0.1086
	y̅ =		357.7714
	sx=		0.9363
	sy =		176.517
	r=		0.3567
slope b1=r*sy/sx=			67.2473
intercept bo=y̅ +r(sy/sx)*(x̅)=			365.0745

y^ =365.0745+67.2473x

4)

n increase of 0.5 in measure of gray matter corresponds to an increases of 33.6236  in number of Facebook friends.

5)

predicted value =67.2473*0.1+365.0745=

371.7992

6)

residual =260-371.7992 =-111.7992

B. lower than
7)

B. No, because 2.5 is beyond the range of the data used to build the regression model.

8)

B. Increasing the measure of gray matter an individual has will increase the number of Facebook friends they have.

C. Measures of gray matter correlate to counts of Facebook friends