Question

The following data lists temperature (x, in degrees Fahrenheit) and sales (y, in dollars) for 15 random days at an ice cream shop. At the 5% significance level, use Excel to test the claim that temperature and ice cream sales are linearly related by specifying the slope estimate, p-value and final conclusion below.

Do not round any intermediate calculations. Round your slope estimate answer to 2 decimal places. Round your p-value to 4 decimal places. Enter a "−" sign in front of any negative answer.

Slope estimate =

p-value =

Final conclusion: The data does not support the claim that temperature and ice cream sales are linearly related.

The data supports the claim that temperature and ice cream sales are linearly related.

Temperature Sales

35 245

57 285

87 348

92 368

56 336

85 510

86 344

62 496

63 441

33 231

56 448

79 553

80 560

57 285

73 511

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.56067478
R Square	0.314356209
Adjusted R Square	0.261614379
Standard Error	96.48980878
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	55491.91841	55491.91841	5.960282542	0.029690482
Residual	13	121033.6816	9310.283199
Total	14	176525.6
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	168.606462	96.97028488	1.738743598	0.10568921	-40.88510206	378.0980261	-40.88510206	378.0980261
Temp	3.428474595	1.404324627	2.441368989	0.029690482	0.394615688	6.462333503	0.394615688	6.462333503

Case 1:

Hypothesis :

H0 : β1 = 0

Ha : β1 not = 0

Test :

Slope estimate = 3.43

F = 5.9603

P value = 0.0297 < 0.05

P value < 0.05, Reject H0

There is enough evidence to conclude that there is significant relation between temperature and ice cream sales

or

There is enough evidence to conclude that temperature and ice cream sales are linearly related

Case 2 :

If temperature is increased by 1 unit then ice cream sales increased by 3.43 units

t = 2.4414

and p value for slope = 0.0297 < 0.05, Reject H0

There is enough evidence to conclude that temperature and ice cream sales are linearly related

Case 3 :

r = 0.5607 which means positive and moderate relation between temperature and ice cream sales

Hypothesis :

H0​: ρ = 0

HA​: ρ not = 0

df = n-2 = 13

r critical = 0.514

r > rc, reject H0

There is enough evidence to conclude that temperature and ice cream sales are linearly related