A quant jock from your firm used a linear demand specificati

A quant jock from your firm used a linear demand specification to estimate the demand for its product and sent you a hard copy of the results. Unfortunately, some entries are missing because the toner was low in her printer. Use the information presented below to find the missing values. Then, answer the accompanying questions. a. Based on these estimates, write an equation that summarizes the demand for the firm\'s product. b. Which regression coefficients are statistically significant at the 5 percent level?

Solution

summary output

R square = (multiple R square)^2

= 0.38*0.38= 0.1444

Adjusted R square = (1-R square)*(N-1) / (N-p-1)

Where N= Total number of observation (=150) and p= Total number of estimators (=2)

Thus Adjusted R square =(1-0.1444)8(150-1) / (150-2-1)

   =0.8672

Analysis of variance table

Total degree of freedom= regression degree of freedom + residual degree of freedom

= 147+2

=149

Sum of square for rgression = total sum of square -residual sum of square

=73807.49-63408.62

=10398.87

Cofficient table

standard error for intercept = estimated value of intercept / t statistic value corrosponding to intercept

= 58.87 / 3.84

=15.33073

t statistic value for price estimate = coefficient value of price / standard error of price estimate

=-1.64/0.85

=-1.92941

cofficient value of income = t statistic value corrosponding to income *standard error of income

=4.64*0.24

=1.1136

a)

Regression equation for demand can be summarized as

Q_x^d= 58.87 - 1.64 * P_x + 1.11 * M

Where

P_x = variable represents price

M= variable represents income

_b)

If the p value observed for the coefficient value is less than 0.05, variable corrosponding to the perticular coefficient will be statistically significant.

As p value observed for intercept coefficent and income coefficient is less than 0.05, thus it can be said that income and intercet value are statistically significannt.