Question

1.)

Hypothesis test for correlation. Use the given data to do the following tasks.

x	y
5	20
6	20
7	15
8	16
9	11
10	11

(a) Calculate the correlation coefficient r.  (use three sig figs)

(b) Find the regression line: y=y=  +  xx. (round values to two decimal places)

(d) Test the claim that there is correlation and find the p-value:  (State answer to three significant figures, which is different than stating values to three decimal places. For our purposes, stating a value to three significant figures is stating the value until there are three non-zero digits after the decimal place.)

(e) Determine whether there is significant correlation. (Use alpha = .05.)

• There is not sufficient evidence to support correlation.
• There is not sufficient evidence to reject correlation.
• There is sufficient evidence to reject correlation.
• There is sufficient evidence to support correlation

2.)

Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
18.7	-7.6
21.7	-8.8
56.3	73.9
14.3	9.7
10.2	-29.1
28.9	6.8
20.6	5.1
43	56.7
27.7	13.3
47.9	63
55.6	54.8
21	14.2

Find the correlation coefficient and report it accurate to three decimal places.
r =

Based on the data, calculate the regression line (each value to three decimal places)

ˆyy^ =  +  xx


Predict what value (on average) for the response variable will be obtained from a value of 35.6 as the explanatory variable.

What is the predicted response value? (Report answer accurate to one decimal place.)

Answer 1

Question 1)

(a) Calculate the correlation coefficient r.

Computational Table:

	X	Y	X2	Y2	XY
	5	20	25	400	100
	6	20	36	400	120
	7	15	49	225	105
	8	16	64	256	128
	9	11	81	121	99
	10	11	100	121	110
Total	45	93	355	1523	662

Correlation coefficient (r):

r = -0.940

b)

For Slope:

b = -2.03

For Intercept:

Where,

a = 15.5 - (-2.03 * 7.5)

a = 30.71

Therefore, the least square regression line would be

d)

Hypothesis:

OR (No linear Correlation)

OR (Positive linear Correlation)

Test statistic:

Degrees of Freedom = n-2 = 6-2 = 4

P-value: 0.005 .....................Using t table

P-value < , i.e. 0.005 < 0.05, That is Reject Ho at 5% level of significance.

Therefore, population correlation coefficient statistically significant at the 5% level of significance.

e)

ANSWER: d. There is sufficient evidence to support correlation