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.
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.
Download the “cigarettes” excel file from the D2L exam page. For this question you are to...
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