Consider our sales regression model. The data is contained as below.

Month	Unit Sales	Price ($)	Adexp ('000$)	Promexp ('000$)
1	73959	8.75	50.04	61.13
2	71544	8.99	50.74	60.19
3	78587	7.50	50.14	59.16
4	80364	7.25	50.27	60.38
5	78771	7.40	51.25	59.71
6	71986	8.50	50.65	59.88
7	74885	8.40	50.87	60.14
8	73345	7.90	50.15	60.08
9	76659	7.25	48.24	59.90
10	71880	8.70	50.19	59.68
11	73598	8.40	51.11	59.83
12	74893	8.10	51.49	59.77
13	69003	8.40	50.10	59.29
14	78542	7.40	49.24	60.40
15	72543	8.00	50.04	59.89
16	74247	8.30	49.46	60.06
17	76253	8.10	51.62	60.51
18	72582	8.20	49.78	58.93
19	69022	8.99	48.60	60.09
20	76200	7.99	49.00	61.00
21	69701	8.50	48.00	59.00
22	77005	7.90	54.00	59.50
23	70987	7.99	48.70	58.00
24	75643	8.25	50.00	60.50

Please estimate the following model

Ln(Sales) = _0 + _1 Ln(Price) + _2 Ln(AdExp) + _3 Ln(PromExp)

where Sales is the unit sales, Price is the price in $, AdExp is the monthly amount of ad expenditure in '000$ and PromExp is the monthly amount of promotions expenditure in '000$

(a) What is the price elasticity of Sales, based on this regression model.

(b) Report and interpret the coefficient ₃.

(c) Test the hypothesis that a 10% increase in AdExp corresponds to a Sales increase of at least 5%.

(d) Predict the Sales when the unit is priced at $8.50, the monthly ad expenditure is 51,000$ and the monthly promotion expenditure is 61,000$.

(e) Build a 95% confidence interval for your prediction.

(f) The company wants to use the regression output to show evidence that the sales in part (d) would be in excess of 73,000 units. Calculate the probability that the sales in part (d) is greater than 73,000 units.