Question

1. Download the “cigarettes” excel file from the D2L exam page. For this question you are to investigate the relationship between the quantity of cigarettes purchased in Pennsylvania, Illinois, and Ohio and various explanatory variables. In your data set you given:

Qty	pC	pR	Income	State
65.4	4.2	2.25	35.8	p
30	10.7	10.5	72.5	i
64.1	4.25	2.49	38.3	o
81.7	3.75	3.33	32.5	i
64.1	3.75	3.18	40.7	o
30.5	10.175	8.5	65.5	p
48.3	7.175	6.25	45.6	p
46.3	9.65	7.25	57.6	i
57.8	4.5	4.5	37.8	o
63.5	3.75	3.9	45.0	p
65.9	4.12	3.51	39.6	p
45.7	7.5	6.5	42.4	p
55.6	5.9	3.5	36.8	i
47.9	8.75	3.3	46.7	o
44.3	8.875	6.2	58.5	p
51.6	7.775	6.2	48.6	o
54.2	7.725	5.85	50.1	p
56.9	4.2	2.01	37.5	i
42.4	8.55	5.7	57.5	o
52.1	6.5	3.45	54.0	p
50	8.54	4.23	55.1	p
57	7.775	4.5	48.8	p
32.9	9.3	6.25	62.5	i
51.6	7.75	4.05	55.0	i
53.8	7.53	4.11	57.1	o
52.5	6.75	4.17	52.2	p
65.3	4.2	3.54	39.5	o
46.8	9.975	5.07	58.2	i
35.8	9.725	5.13	68.5	p
58.1	4.86	3.3	41.4	o

Qty = number of packs of cigarettes purchase

pC = the price of a pack a cigarettes in dollars

pR = the average price of all other goods (non-cigarettes)

Income = income in dollars

State = p if the observation is from Pennsylvania, i if the state is Illinois, and o if the state is Ohio.

1. Convert the State variable into dummy variables that can be used in regression analysis and then estimate a multiple regression model in which the quantity of cigarettes purchased depends on the price of cigarettes, the price of all other goods, income, and the state in which they were purchased. (5 points)

2. Interpret the estimated coefficients. Note any discrepancies from your a priori beliefs. (5 points)

3. Is the overall regression model a good one? Why or why not? (Hint: Look at adjusted R-squared) Are the dependent variables JOINTLY significant? Explain. (5 points)

4. For each of the estimated coefficients, conduct a hypothesis test to determine if the coefficient is statistically different from zero. Write the null and alternative hypothesis for each, and whether you accept or reject the null hypothesis. EXPLAIN how you arrived at your answer. Use a level of significance of 0.05. (5 points)

Answer 1

a)

first we will make state variable as dummy variable

we will code

if state is 'p' then state =0

if state is 'i' then state =1

if state is 'o' then state =2

Qty	pC	pR	Income	State
65.4	4.2	2.25	35.8	2
30	10.7	10.5	72.5	1
64.1	4.25	2.49	38.3	o
81.7	3.75	3.33	32.5	1
64.1	3.75	3.18	40.7	o
30.5	10.175	8.5	65.5	2
48.3	7.175	6.25	45.6	2
46.3	9.65	7.25	57.6	1
57.8	4.5	4.5	37.8	o
63.5	3.75	3.9	45	2
65.9	4.12	3.51	39.6	2
45.7	7.5	6.5	42.4	2
55.6	5.9	3.5	36.8	1
47.9	8.75	3.3	46.7	o
44.3	8.875	6.2	58.5	2
51.6	7.775	6.2	48.6	o
54.2	7.725	5.85	50.1	2
56.9	4.2	2.01	37.5	1
42.4	8.55	5.7	57.5	o
52.1	6.5	3.45	54	2
50	8.54	4.23	55.1	2
57	7.775	4.5	48.8	2
32.9	9.3	6.25	62.5	1
51.6	7.75	4.05	55	1
53.8	7.53	4.11	57.1	o
52.5	6.75	4.17	52.2	2
65.3	4.2	3.54	39.5	o
46.8	9.975	5.07	58.2	1
35.8	9.725	5.13	68.5	2
58.1	4.86	3.3	41.4	o

Regression Equation

State          
0   Qty   =   91.11 - 2.39 pC - 1.116 pR - 0.355 Income
            
1   Qty   =   92.71 - 2.39 pC - 1.116 pR - 0.355 Income
            
2   Qty   =   91.85 - 2.39 pC - 1.116 pR - 0.355 Income

2)

Interpret the estimated coefficients

=91.37

It can be interpretated as it is the average  number of packs of cigarettes purchase .

= If the price of a pack a cigarettes in dollars increases by 1 unit then on an average decrease in number of packs of cigarettes purchase will be 2.313units when remaining independent variable kept constant.

= If the average price of all other goods (non-cigarettes increases by 1 unit then on an average decrease in number of packs of cigarettes purchase will be 1.097 units when remaining independent variable kept constant.

=  If the income in dollars increases by 1 unit then on an average decrease in number of packs of cigarettes purchase will be 0.365 units when remaining independent variable kept constant.

3)

Is the overall regression model a good one?

Model Summary
S	R-sq	R-sq(adj)	R-sq(pred)
5.26023	82.76%	79.17%	71.62%

yes overall mode is good because both are greater than 70 %.

R-sq	R-sq(adj)
82.76%	79.17%

Are the dependent variables JOINTLY significant?

here p-value for regression is 0  < 0.05 level of significance so we reject the null hypothesis and conclude that the dependent variables JOINTLY significant.

4)

Coefficients
Term	Coef	SE Coef	T-Value	P-Value	VIF
Constant	91.11	5.26	17.33	0
pC	-2.39	1.01	-2.38	0.026	5.47
pR	-1.116	0.805	-1.39	0.178	2.43
Income	-0.355	0.204	-1.74	0.095	4.86
State
1	1.6	2.67	0.6	0.554	1.51
2	0.73	2.35	0.31	0.757	1.47

by observing all p-values all p-values are > 0.05 so we accept the null hypothesis and conclude that pC, pR, Income, State are not significant variables.