Exam #1

Question 1

Y=a+b1X1 + b2X2 + B3X3 + b4X4
Y=-19.672+ (-0.001*X1) + (1.740*X2) + (0.410*X3) + (2.036*X4) + (-.034*X5)

Step 3

B1 is Negative: Number of retail outlets. An inverse association between retail Outlets and annual sales. An increase one retail outlet will result in a decrease in sales of .001 dollars.

B2 is positive: Number of automobiles registered. Positive association between the number of Automobiles registered and Annual sales. An increase in one registered automobile will result in an increase in sales of 1.740 dollars.

B3 is positive: Personal income. Positive association between the personal income and annual sales. An increase in personal income will result in an increase in sales of 0.410 dollar.

B4 is positive: Average age of automobiles. Positive association between the average age of automobiles and sales. An increase in the average age of automobiles will result in an increase in sales of 2.036 dollars.

B5 is negative: Number of supervisors. An inverse association between the number of supervisors and sales. An increase in supervisor will result in a decrease in sales of 0.034 dollars.

Step 4
Y=-19.672+ (-0.001*X1) + (1.740*X2) + (0.410*X3) + (2.036*X4) + (-.034*X5)
Y= -19.672 + (-0.001*1,739) + (1.740*9,270,000) + (0.410*85,400,000,000) + (2.036*3.4) + (-.034*9)
Y=-19.672 + (-1.739) + (16,129,800) + (35,014,000,000) + (6.922) + – (0.306)
Y= 35184129785.204

Number of Retail Outlets (X1)= 1,739
Number of Automobiles Registered(X2)= 9,270,000
Personal Income (X3)= 85,400,000,000
Average Age of Automobiles (X4)= 3.5
Number of Supervisors (X5) = 9
Point elasticity= Ex1 = ?Y/?X * X/Y = -1.739/Y = -.94 x10^-11 Inelastic
Point elasticity= Ex2 = ?Y/?X * X/Y = 16,129,800/Y =4.58×10^-4 Elastic
Point elasticity= Ex3 = ?Y/?X * X/Y = 35,014,000,000/Y= 1.00 Elastic
Point elasticity= Ex4 = ?Y/?X * X/Y = 6.922 /Y= 7.97×10^-10 Elastic
Point elasticity= Ex5 = ?Y/?X * X/Y= -0.306/Y= 8.70 x10^-12 Elastic

Step 5
t1= -0.238 is not significant
t2= 3.146 significant
t3= 9.348 Significant
t4= 2.318 Significant
t5= -0.183 is not significant

X2(number of automobiles registered), X3(personal income), X4(average age of automobiles) are statistically significantly because their absolute t values are greater than 2. The other two variables X1 and X5 are not.

We can be 95% confident that X2, X3 and X4 truly have an impact on the sales

B1 and B5 are nonzero numbers simply because of fluke sales.

Any estimated coefficient of variable passes the t-test, we can be confident that the variable does have an impact on demand.

R^2 = 0.9943
Which means about 99% of the variation in the demand for sales can be accounted for by the variation in those 5 variables (number of retail outlets, number of automobiles registered, personal income, average age of automobiles, number of supervisors).
Conclusion:

The number of automobiles registered, personal income, and the average age of automobiles are the key factors influencing sales. This can be seen due to their high significance (as indicated by high t-scores and low p-values) and the relatively high elasticities (indicating high impact on sales))

Question#2