Question

6. Consider the following data of the number of hours 12 students spent online during the weekend and the scores of each student who took a test the followingMonday.

Hrs spent online(x)	0	1	2	3	3	5	5	5	6	7	7	10
Test scores(y)	96	85	82	74	95	68	76	84	58	65	75	50

a. Find the sample linear correlation coefficient and interpret it.

b. Is the population correlation coefficient significant? [ use α= 0.05]

c. Find the equation of the regression line. What is the slope of the line? Interpret

this value in the context?

4. What is the coefficient of determination? Interpret the result?

5. If ? is 3.5 hours, what would you expect ? to be?

6. If ? is 5 hours, what would you expect ? to be?

7. g. If ? is 20 hours, what would you expect ? to be?

Answer 1

a) We calculate r=-0.8312962. Hence a strong negative association between x and y exists.

b)Null hypothesis: rho(population correlation coeff)=0

Alternative hypothesis: rho(population correlation coeff) is different from 0

Test statistic

We reject if |T|>t_.025,n-2, n=sample size=12

We compute T= -4.7295, df = 10 and p-value = 0.0008048(<.05)

Hence we reject the null and  the population correlation coefficient is significant at 5% level.
c) We calculate the regression equation as

y=93.970-4.067 x

The slope of the line is -4.067

Then for one hour increase in online staying, the test score is decreased by 4.067, on average.

d)Coefficient of determination=r²=.6911

Thus 69.11% variation in data is explained by the fitted regression line.

e) x=3.5 implies expected y=93.970-4.067*3.5= 79.7355

f) x=5 implies expected y=73.635

g)x=20  implies expected y=12.63