# Quiz 4: Basic Estimation Techniques

The given equation of BS ld's sales is, Here, the sales ( S ) of BS ld is a function of V Corporation's advertisement expenditure ( A ) and three biggest rival's advertisement expenditure ( R ). a. The marketing director expects coefficients a and b to be positive as they effect directly the sales and coefficient b to be negative as it negatively affects the sales of Bright Side Detergents. b. Coefficient " a " explains that the sales would be equal to a when the advertisement expenditure of Vanguard and Rivals are zero. Coefficient " b " states that an increase in ( A ) would increase the sales S by b times. Coefficient " c " explains that an increase in ( R ) will decrease the sales by c times. c. The p-value of V Corporation's advertisement expenditure ( A ) is 1.28%. This means there is more than 98% confidence interval. Therefore Vanguard's advertisement has significant effectiveness on sales of Bright Side Detergents. d. The p-value of Rival's advertisement expenditure ( R ) is 9.27%, which is less than 10%. This means there is more than 90% confidence interval. Therefore Rival's advertisement has significant effectiveness on sales of Bright Side Detergents. e. Coefficient of determination defines the explained variations in regression analysis. Given that R square is.2247, the explained variation is 0.2247. The unexplained variation is, • Therefore, the unexplained variation is 0.7753. • Other explanatory variables such as price of product, price of the substitute product etc. could be added to make the analysis more appropriate. f. Given information A =$40,000 a =175086 b =0.855 c =-0.284 R =$100,000 The value of sales of BS ld's detergents would be: Therefore, the expected level of sales each week is $180,886.

The given regression equation of relation between the average premium ( P ) and percent people for proposition 103 ( V ) is, a. F-test is used to test the overall regression equation for its statistical significance. Here, k-1= first degree of freedom and = second degree of degree of freedom. Given information = 17 = 2 Thus, And, • The F table shows a value of 4.54 with 1 and 15 degrees of freedom in 5% significance value or 95% confidence interval. • The calculated F ratio given in the table is 42.674, which is much greater than the table value. Therefore, the regression equation is statistically significant at 5% level of significance. b. The intercept estimate "a" can be tested for its level of significance with the help of t-test. • The t value can be calculated by dividing parameter value and standard error. • The t table value for 95% confidence interval with 15 degrees of freedom is 2.121. • The calculated value of 25.39 of t is far greater than the table value. • Therefore the intercept is statistically significant. If preposition 103 (V) has no effect on premiums (P) , then the percent of voters for 103 would be 53.682. This is the value of intercept and when P is zero, the value of V is equal to the value of intercept a. c. Given: Value of b is -0.528. Now, calculate the value of b at 95% confidence interval as follows: • The t table value for 95% confidence interval with 15 degrees of freedom is 2.121. • The calculated value 6.88 of t is far greater than the table value. • Therefore the slope is statistically significant. "b" is the slope that determines the change in value of V due to change in P. Therefore, if the value of P decreases by 10%, then the value of V decline by 5.28%.

The given regression equation of relation between earning ( E ) and number of tickets sold ( N ) is, a. Movie ticket sale and earnings are connected by slope parameter b. If we run a t-test on b at 95% confidence interval, we can arrive at the level of effectiveness of movie tickets sold on earnings. • The table value of t at 13 degrees of freedom (15-2) is 2.160 • The calculated value of t is equal to 3.78, calculated as, . • At 95% confidence interval, the value of b is significant. Thus, movie tickets have effect on the value of annual earnings. b. "b" is the slope that determines the change in value of E due to change in N. Therefore, an increase of 100,000 in number of tickets sold increases the earnings by $3,231,000. c. The earning can be calculated by using the below equation and substituting the value of N, a and b: If number of tickets sold is 950,000, then the earning is $55,736,500.