Question

1. The scores of 10 people on standardized scales of introversion and shyness are shown below (high scores on each scale indicate high introversion and high shyness)

Person	Introversion	Shyness
1	17	22
2	6	4
3	12	10
4	13	8
5	19	11
6	20	18
7	9	10
8	4	3
9	8	10
10	21	16

a. Make a scatterplot of the data. What is the type of relationship?

b. compute r and test it for significance? How much of the variability is accounted for by r?

c. Compute the regression equation for Y’

d. Use the equation to predict the shyness score of a person with an introversion score of 15

2. A group of students was asked to estimate the amount of time each spend per day reading the newspaper. Then each student was given a 20-item recognition test of current events. The paired scores are:

Student	Time in minutes	Score
A	25	12
B	40	13
C	55	18
D	10	8
E	5	5
F	5	3
G	30	10
H	45	15

a. Compute r and test it for significance? How much of the variability is accounted for by r?

c. Compute the regression equation for Y’

Answer 1

a)

Using Excel

select cells for both x and y

Insert -> scatter

b)

r = 0.8051   {use correl function in excel}

t = 3.8399

p-value = P(T > |TS|) = 0.0049

P-value

for two-tailed

p-value = P(t > |TS|)

= t.inv.2t(abs(TS),df)

if p-value < alpha, we reject the null hypothesis

if p-value > alpha, we fail to reject the null hypothesis

since p-value < alpha, we reject the null hypothesis

r^2 = 64.83%

64.83% of the variability is accounted for by r

c)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.80515394
R Square	0.648272867
Adjusted R Square	0.604306975
Standard Error	3.748532908
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	207.1880083	207.1880083	14.74490436	0.004947825
Residual	8	112.4119917	14.05149896
Total	9	319.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.083704363	2.888912358	0.375125386	0.717317287	-5.57813948	7.745548
Introversion	0.784208964	0.204225902	3.839909421	0.004947825	0.31326319	1.255155

y^ = 1.0837 + 0.7842 * x

d)

when x = 15

y^ = 1.0837 + 0.7842 * 15

= 12.8468