1. Novo Nordisk A/S, a Danisg firm, sells insulin and other drugs worldwide. Act

Question

1. Novo Nordisk A/S, a Danisg firm, sells insulin and other drugs worldwide. Activella, an estrogen and progestin hormone replacement therapy sold by Novo-Nordisk, is examined using 33 quarters of data

Y = -204+.34X1-.17X2

(17.0) (-1.71)

Where Y is quarterly sales of Activella, X1 is the Novo's advertising of the hormone therapy, and X2 is advertising of a similar product by Eli Lilly and Company, Novo-Nordisk's chief competitor. The parentheses contain t-values. Addition information is: Durbin-Watson = 1.9 and R2= .89. According to t distribution table , t .05,31=1,6955

Using the data for Novo-Nordisk, which is correct?

A. Both X1 and X2 are statistically significant.

B. Neither X1 nor X2 are statistically significant.

C. X1 is statistically significant but X2 is not statistically significant.

D. X1 is not statistically significant but X2 is statistically significant.

E. The Durbin-Watson statistic shows significant problems with autocorrelation.

2. Which is NOT true about the coefficient of determiniation?

A. As you add more variables, the R-square generally rises.

B. As you add more variables, the adjusted R-square can fall.

C. If the R-square is above 50%, the regression is considered significant.

D. The R-square gives the percent of the variation in the dependant variable that is explained by the independent variables.

E. The higher is the R-square, the better is the fit.

3. Table: Sherwin-Williams Company new Data

Observations Sales Promotional Expenditures Selling Price Disposable Income

i y A P M

1 160 100 15 19

2 200 160 14 17.5

3 140 50 16.5 14

4 190 190 14.5 20

5 130 90 17 15.5

6 160 70 16 14.5

7 200 140 15 21.5

8 150 110 18 18

9 210 200 12 18.5

10 190 100 15.5 20

Total 1750 1250 151 179.5

Mean 175 125 15.1 17.95

A. What is regression equation for paint sales using multiple linear regression model?

B. If A=180, P=$14, and M= 20, what is an approximate 95 percent prediction interval for paint sales?

Explanation / Answer

(1) When the t-value for a coefficient is equal to or greater than 2, we can say that the variable is statistically significant.

Here, t-value for X1 is 17 > 2 but t-value for X2 is - 1.71 < 2.

So, X1 is statistically significant while X2 is not.

Correct option (C)

(2) Option (B) is incorrect.

as the number of variables increase, R2 also increases, it does not fall.

(3)

(a) Regression Model.

The regression summary output is as follows.

So the regression equation is:

Y = 240.34 + 0.06A - 10.01P + 4.44M

(b) A = 180, P = 14, M = 20

Y = 240.34 + (0.06 x 180) - (10.01 x 14) + (4.44 x 20)

= 240.34 + 10.8 - 140.14 + 88.8

= 199.8

This is the sample mean.

t-value for 95% confidence & 9 degrees of freedom is 2.262.

Standard error = 13.58 (From summary output)

So, confidence interval = Sample mean ± (t) x Standard error

= 199.8 ± (2.262 x 13.58)

= 199.8 ± 30.72

= 169.08 to 230.52

SUMMARY OUTPUT Regression Statistics Multiple R 0.920075183 R Square 0.846538343 Adjusted R Square 0.769807515 Standard Error 13.57975544 Observations 10 ANOVA df SS MS F Significance F Regression 3 6103.541453 2034.514 11.03257 0.00743593 Residual 6 1106.458547 184.4098 Total 9 7210 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 240.3418664 79.69164471 3.015898 0.023521 45.34343689 435.3402959 45.34343689 435.3402959 A 0.058674793 0.164876515 0.355871 0.734115 -0.3447635 0.462113091 -0.344763504 0.462113091 P -10.00716179 4.160789492 -2.40511 0.052925 -20.1882469 0.173923309 -20.18824689 0.173923309 M 4.435205441 2.350952139 1.886557 0.108167 -1.3173672 10.18777808 -1.317367198 10.18777808

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