Question

The Quick Sell car dealership has been using 1-minute spot ads on a local TV station. The ads always occur during the evening hours and advertise the different models and price ranges of cars on the lot for that week. During a 10-week period, a Quick Sell dealer kept a weekly record of the number x of TV ads versus the number y of cars sold. The results are given in the table.

Is there a significant correlation between the number of ads and the number of cars sold?

											Total
x (hrs.)	6	20	0	14	25	16	28	18	10	8	145
(gal.)	15	31	10	16	28	20	40	25	12	15	212
x2
y2
xy

a) Calculate r.

b) Find the line of prediction by calculating b and a.

c) Given the equation of the line of prediction, predict the number of cars sold if there are 12

ads in a given week.

d) If the hypotheses for this problem are Ho: ρ = 0 and H1: ρ >0 (more ads mean more cars

sold), Reject or Fail to Reject the Ho at the 0.05 level of significance.

Answer 1

using excel>data>data analysis>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.996145002
R Square	0.992304864
Adjusted R Square	0.991449849
Standard Error	5.385418577
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	33659.70267	33659.70267	1160.570019	7.98224E-11
Residual	9	261.0245993	29.00273325
Total	10	33920.72727
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.502108993	1.970702515	0.254786803	0.804614205	-3.955929818	4.960147803
x (hrs.)	1.443023452	0.042358221	34.06713987	7.98224E-11	1.347202498	1.538844406

x (hrs.)	6	20	0	14	25	16	28	18	10	8	145
y(gal.)	15	31	10	16	28	20	40	25	12	15	212
x2	36	400	0	196	625	256	784	324	100	64	21025
y2	225	961	100	256	784	400	1600	625	144	225	44944
xy	90	620	0	224	700	320	1120	450	120	120	30740

a) the value of the correlation coefficient is 0.9962

b) the line of prediction is

y = 0.5021+1.4430x

c) Given the equation of the line of prediction, the number of cars sold if there are 12

is 0.5021+1.4430*12 =17.8181 ads in a given week.

d) If the hypotheses for this problem are Ho: ρ = 0 and H1: ρ >0

t= = 34.31

p value is 0.000

Reject Ho at the 0.05 level of significance.