Question

A linear industry demand function of the firm’s product was estimated using regression analysis. The results of this estimation are as follows: Q = a + bX where X is product’s own price. The team will use the results of the model only at confidence level = 90.00 %.

Dependent Variable	Y	R-Square	F-Ratio	P-Value On F
Observations	10	0.5223	8.747	0.0187
Variable	Parameter Estimate	Standard Error	T-Ratio	P-Value
Intercept	800	189.125	4.23	0.0029
X	-2.5	0.85	-2.94	0.0187

1. What do the parameter estimates mean as given in output table in terms of their value and sign?
2. What is the interpretation of R² value given in output table?
3. Why don’t you see multiple R² in this table?
4. What is the meaning of standard error of X here?
5. How is the t-statistic for X used ?

Only this information is given to solve this.

Answer 1

a)

*Intercept =800

This indicates the demand for the product when its price ( X) is zero

* Value of parameter of X =-2.5

This indicates the change in Y when X is increased by one unit

Here this indicates the change in demand when price increases by unit

Sign is negative, which means that demand will reduce with the increase in price.

When price increases by 1 unit, impact on demand in the form of reduction or decline is 2.5 .

b) R square =0.52

If shows the percentage change in Y explained by the change in X

Here, 52 percent of the change in demand for the Product can be explained by the change in price.

c) Multiple R square shows Change in dependent variable that can be explained by two or more variables together.

Here, it isn't used because there is only one explanatory variable in the regression equation. We are dealing with a single linear regression model.

d) lt shows the accuracy of the regression model. Average distance that the observed values fall from the regression line.

Here standard error of X is lower . lts 0.85 , even less than 0ne.So estimated parameter is precise and close to population.

e) t statistic can be computed by dividing the coefficient of X with standard error . t statistic for X is used to conduct hypothesis tests on the regression coefficients obtained.