Question

. Using your data file Ice Cream, find:

            Temperature = Independent Variable; Sales = Dependent variable

Temperature	Sales
63	1.52
70	1.68
73	1.80
75	2.05
80	2.36
82	2.25
85	2.68
88	2.90
90	3.14
91	3.06
92	3.24
75	1.92
98	3.40
100	3.28
92	3.17
87	2.83
84	2.58
88	2.86
80	2.26
82	2.14
76	1.98

           a. What is an appropriate null hypothesis for Regression Analysis?

           b. What is the test statistic (F) for the regression?

           c. What is the p value for the regression?

           d. What is your conclusion concerning the null hypothesis? Reject / Not Reject?

           e. What is the value of the R Square?

            f. Interpret R Square (what does it mean)?

            g. What is the value of the slope?

            h. What is the value of the y intercept?

Answer 1

Solution:

Given data:

Temperature	Sales
63	1.52
70	1.68
73	1.8
75	2.05
80	2.36
82	2.25
85	2.68
88	2.9
90	3.14
91	3.06
92	3.24
75	1.92
98	3.4
100	3.28
92	3.17
87	2.83
84	2.58
88	2.86
80	2.26
82	2.14
76	1.98

From given data we first do regression analysis using excel. The output is,

Regression Analysis
	r²	0.940	n	21
	r	0.970	k	1
	Std. Error	0.146	Dep. Var.	Sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	6.3541	1	6.3541	297.65	4.59E-13
Residual	0.4056	19	0.0213
Total	6.7597	20
Regression output				confidence interval
variables	coefficients	std. error	t (df=19)	p-value	95% lower	95% upper
Intercept	-2.5350	0.2952	-8.587	5.77E-08	-3.1529	-1.9171
Temperature	0.0607	0.0035	17.253	4.59E-13	0.0534	0.0681

a) Null hypothesis for Regression Analysis

H₀ : β₁ = 0

That is, the observed relationship is not statistically significant.

b)

F statistic = 297.65

c)

P-value for the regression is , P-value = 4.59E-13 0

d)

Conclusion: P-value < 0.05, hence reject H0. Because the p-value is so small. Hence, the observed relationship is statistically significant.

e)

Here, R² = 0.940 = 94%

f)

94% of sales that can be explained by temperature.

g)

Slope = 0.0607

h)

Intercept = -2.5350

Done