TWO QUESTIONS - PLEASE USE 2 SEPARATE COMMENTS, THANKS 1. The below table presen
ID: 3331058 • Letter: T
Question
TWO QUESTIONS - PLEASE USE 2 SEPARATE COMMENTS, THANKS
1. The below table presents data collected on sales (average sales prices and quantity sold) of electric vehicles for the 3-month period (Jan-March 2017) from a random selection of 16 markets across the country, and the output of a linear regression of the data.
What is the linear consumer demand equation, and is it consistent with your expectation?
Does the linear regression line represent a ‘good fit’ of the observed data points?
Is the slope of the linear regression line significantly different from 0?
Price
Quantity
74800
10
83000
7
92500
6
45000
18
123000
3
105250
3
65250
14
54500
17
75450
13
42500
19
123200
5
122100
4
112540
8
95750
7
83250
5
137450
2
Slope: -4,720.8 (st. error = +569.7)
Y-intercept: 131,323.0 (st. error = +5914.9)
R2 = 0.83
F-value = 68.68; df = 1,14; p-value <0.001
t-value = -8.29; df = 14; p-value <0.001
2. Subsequent to the initial analysis (outlined above in question #1), car dealers in each of the local markets being evaluated provided additional data on the average income of consumers in their local market, the average sale price of residential solar systems ($$$ / square foot) in the same local market, and the average value of local subsidies to consumers for purchasing electric vehicles. The below table presents data collected on those variables and the output of a multiple linear regression of the data.
What is the consumer demand equation, and is it consistent with your expectation?
Did the inclusion of additional x-variables (i.e., consumer income, sale price for solar, subsidies, etc.) improve the explanatory power of the regression equation? How can you tell?
Does the linear regression line produced by this analysis represent a ‘good fit’ of the observed data points?
For which x-variables (quantity of EVs sold, average income, sale price solar and subsidies) is the slope of the linear regression line significantly different from 0?
Please explain the observed relationship between average consumer income and the sale price of EVs.
Price
Quantity
Average income
Sale prices for solar
Subsidies
$74,800.00
10
$225,000.00
1250
1750
$83,000.00
7
$265,000.00
1950
2250
$92,500.00
6
$260,000.00
1950
2000
$45,000.00
18
$175,000.00
800
1750
$123,000.00
3
$350,000.00
2500
1850
$105,250.00
3
$375,000.00
2500
1500
$65,250.00
14
$160,000.00
1300
2000
$54,500.00
17
$175,000.00
1250
1900
$75,450.00
13
$165,000.00
1600
1850
$42,500.00
19
$185,000.00
950
1925
$123,200.00
5
$250,000.00
2900
1850
$122,100.00
4
$345,000.00
2750
2000
$112,540.00
8
$295,000.00
2250
1900
$95,750.00
7
$275,000.00
2100
1850
$83,250.00
5
$325,000.00
2700
1900
$137,450.00
2
$425,000.00
4000
2000
Slope(Quantity): -8.33 (st. error = +19.70)
Slope(Average income): 20.18 (st. error = + 8.64)
Slope(Sale price for solar): -0.06 (st. error = + 0.09)
Slope(Subsidies): -2838.27 (st. error = + 1262.97)
Y-intercept: 105,009.0 (st. error = +50279.02)
R2 = 0.89
F-value = 22.10; df = 4,11; p-value <0.01
t-value(Quantity) = 0.42; df = 11; p-value > 0.05
t-value(Average income) = 2.34; df = 11; p-value <0.05
t-value(Sale price for solar) = 0.66; df = 11; p-value > 0.05
t-value(Subsidies) = 2.25; df = 11; p-value < 0.05
Price
Quantity
74800
10
83000
7
92500
6
45000
18
123000
3
105250
3
65250
14
54500
17
75450
13
42500
19
123200
5
122100
4
112540
8
95750
7
83250
5
137450
2
Explanation / Answer
Answer to question# 1)
The demand equation is as follows
Demand = 131323 - 4702.8 * Price
.
In order to find whether it is a good fit or not , we observe the R square value
The r square value is 0.83
this implies that the price is able to explain 83% of the variation in the demand of the vehicle , indicating that there is astrong relation between the variables , and the model is a good fit for the two variables
.
Significance of slope can be measured as follows
We get T value = -8.29 , with a p value < 0.001
since the P value is less than 0.05 , we consider the slope to be signficantly different from 0
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