Question

2. A student collected data on the number of large pizzas consumed, y, while x students were watching a professional football game on TV. The data from five games are given in table below. Number of students, x 2 5 6 3 4 Number of large pizzas, y 1 6 10 3 5 Please show work for full credit.

(e) Interpret your interval from part (d). (f) Calculate r2 (follow steps on page 92).

(g) Interpret r2.

(h) Compute linear correlation coecient r (follow steps on page 93).

(i) Interpret r.

Answer 1

using excel>data>data analysis >Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.97913
R Square	0.958696
Adjusted R Square	0.944928
Standard Error	0.795822
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	44.1	44.1	69.63158	0.003608
Residual	3	1.9	0.633333
Total	4	46
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-3.4	1.067708	-3.18439	0.049925	-6.79792	-0.00208
x	2.1	0.251661	8.344554	0.003608	1.299102	2.900898

(f) R2 =0.9587

(g) About 95.87% variation in number of large pizzas can be explained by the Number of students watching a professional football game on TV.

(h) the linear correlation coefficient r = 0.9791

i) there is a strong positive linear relationship between number of large pizzas and the Number of students watching a professional football game on TV.