Question

Question 2 You will need statistical software to complete this question. From UTS:Online Assessment-Assignment B, download the data set icecream2019.csv. The data set contains 12 months of data. The key variables are described as follows: Sales Per-capita ice-cream sales during the month Rain-average rainfall during the month (in mm) Maxtemp average daily maximum temperature (in degrees Celsius) during the month (a) (lpt) Generate the logarithm of each of the three variables. Use software to construct the following three scatter plots and briefly describe each: 1) Ln(rain) on the x-axis and In(sales) on the y-axis 2) Ln(maxtemp) on the x-axis and In(sales) on the y-axis 3) Ln(maxtemp) on the x-axis and In(rain) on the y-axis (b) (1pt) Estimate a log-log model of ice-cream sales, using Ln(rain) as the only regressor. Report the SRL, standard errors, t-statistics, p-values, R-square, and number of observations in a compact format. (c) (lpt) Provide an interpretation for the slope coefficient. Does the slope estimate make sense? Briefly explain. (d) (1 pt) Suppose the population model is Ln(sales)-po +p/Ln(rain) + β2* Ln(maxtemp) + u, where βι, β2t0. Estimate a log-log model of ice-cream sales. using Ln(rain) and Ln(maxtemp) as regressors. Report the SRL, standard errors, t- statistics, p-values, R-square and number of observations in a compact format. (e) (lpt) Using the descriptive evidence found in part (a) (Note: the sample correlation between In(rain) and In(maxtemp) is 0.89.), compare the estimation results of part (b) with part (d) and explain the difference s). Where does the difference come from? What is the name of the problem arising in part (b)? Which CLRM assumption does the model in part (b) violate? Insert Draw Page Layout Formulas Data Review Home Mer В 1 U.11.6- Paste Alignment Font Clipboard. A1 1[sales 2 1.39004 3 0.958718 4 1.22137 maxtemp month rain 1 63.9 2 76.9 14.4 13.5 17.15 85.1 3 4 102.1 20.65 5 121.9 232 5 1.4598 6 1.52808 7 1.60311 8 1.90125 25.35 132.2 6 7 113.5 27.65 8 142.3 28.6 9 147.2 25.95 9 1.72883 10 1.47369 22.2 155.5 11 1.21093 10 18.5 103.8 12 1.38642 13 1.25854 11 15 12 83.9 14 15 17 18 19 20 21 23 24 25 26 27 28 29 30 31 ! icecream2019

Answer 1

(a) The logarithm transformation looks as follows -

month	Sales	rain	maxtemp	ln(sales)	Ln(rain)	Ln(maxtemp)
1	1.39004	63.9	13.5	0.329333	4.157319	2.602689685
2	0.958718	76.9	14.4	-0.04216	4.342506	2.667228207
3	1.22137	85.1	17.15	0.199973	4.443827	2.841998174
4	1.4598	102.1	20.65	0.378299	4.625953	3.027715319
5	1.52808	121.9	23.2	0.424012	4.803201	3.144152279
6	1.60311	132.2	25.35	0.471945	4.884316	3.23277873
7	1.90125	113.5	27.65	0.642512	4.731803	3.319625728
8	1.72883	142.3	28.6	0.547445	4.957938	3.353406718
9	1.47369	147.2	25.95	0.387769	4.991792	3.25617161
10	1.21093	155.5	22.2	0.191389	5.046646	3.100092289
11	1.38642	103.8	18.5	0.326725	4.642466	2.917770732
12	1.25854	83.9	15	0.229952	4.429626	2.708050201

1. Scatter plot of ln(Sales) and Ln(rain) -

Based on scatter plot, a positive relationship is observed between ln(rain) and ln(sales).

2. Scatter plot of ln(maxtemp) and Ln(Sales) -

Based on scatter plot, a positive relationship is observed between ln(maxtemp) and ln(sales).

3. Scatter plot of ln(maxtemp) and Ln(rain) -

Based on scatter plot, a positive relationship is observed between ln(maxtemp) and ln(rain).

(b) Below the SRL model where ln(sales) is regressed on ln(rain) -

Below is the output in compact format:

Dependent variable: Ln(Sales)	Coefficients	Standard Error	t Stat	P-value
Intercept	-1.0686	0.8404	-1.2715	0.2323
Ln(rain)	0.3017	0.1796	1.6796	0.1240

(c) The slope coefficient is positive. Everything else held constant, a 1% change in rain results in 0.3017% change in Sales. The coefficient however is not statistically significant at 10%, 5% or even 1% level of significance.

PS: According to HOMEWORKLIB RULES, in the event of multiple sub-parts only first 4 are attempted. However, you may re-post the question for further parts.