Question 1

Which of the following best describes the purpose of the method of least squares in linear regression analysis?

Accepted Answer

To minimize the sum of the squared distances from each sample data point to the sample regression line.

Question 2

In the simple linear regression equation $$Y = a + bX$$, what does the parameter $$b$$ represent?

Accepted Answer

The change in $$Y$$ associated with a one-unit change in $$X.$$

Question 3

A regression analysis of monthly sales ($$Y) on $$advertising expenditures ($$X) $$yields the sample regression line $$\hat{Y} = 11,573 + 4.9719X. $$What is the predicted sales value when advertising expenditures are $6,000?

Accepted Answer

$$\41$$,405.40$

Question 4

Which of the following statements about the $$R^2$$ statistic is TRUE?

Accepted Answer

$$R^2$$ measures the proportion of the total variation in the dependent variable explained by the regression model.

Question 5

A researcher tests the null hypothesis that the slope coefficient $$b in a $$regression is zero. The estimated $$b is$$ $$2.5$$ with a standard error of $$0.5. $$What is the value of the $$t-$$statistic?

Accepted Answer

$$t = 5.0$$

Question 6

Which of the following best describes the meaning of a p-value of $$0.03$$ for a regression coefficient, when the significance level is $$0.05$$?

Accepted Answer

The coefficient is statistically significant at the 5% level.

Question 7

In a multiple regression model, what does the coefficient of an explanatory variable represent?

Accepted Answer

The change in the dependent variable associated with a one-unit change in that explanatory variable, holding all other variables constant.

Question 8

Which of the following is a key reason for using Adjusted $$R^2$$ instead of $$R^2 in $$multiple regression?

Accepted Answer

Adjusted $$R^2$$ penalizes for adding unnecessary variables and is a more reliable measure of model fit.

Question 9

A quadratic regression model is appropriate when:

Accepted Answer

The scatter plot of $$Y$$ versus $$X is U-$$shaped or n-shaped.

Question 10

Which of the following is the correct transformation for a log-linear regression model of the form $$Y = aX^bZ^c$$?

Accepted Answer

$$\ln Y = (\ln a) + b(\ln X) + c(\ln Z)$$

Question 11

Suppose a regression output shows an $$F-$$ratio of $$16.30$$ with a significance $$p-$$value of $$0.01. $$What does this indicate about the regression model?

Accepted Answer

The independent variables, as a group, explain a significant portion of the variance in the dependent variable.

Question 12

If the absolute value of the $$t-$$statistic for a regression coefficient is less than the critical $$t$$ value, what is the correct conclusion?

Accepted Answer

The coefficient is not statistically significant.

Question 13

Which of the following best describes a Type I error in the context of regression analysis?

Accepted Answer

Rejecting a true null hypothesis.

Question 14

A time series data set is best described as:

Accepted Answer

Data for the dependent and explanatory variables collected over time for a specific firm.

Question 15

In regression analysis, what is the 'residual'?

Accepted Answer

The difference between the actual and fitted values of $$Y.$$

Question 16

Which of the following is NOT a correct interpretation of the intercept parameter $$a in $$the regression equation $$Y = a + bX$$?

Accepted Answer

It measures the change in $$Y$$ for a one-unit change in $$X.$$

Question 17

A regression model has an $$R^2 of$$ $$0.80. $$What does this mean in practical terms?

Accepted Answer

80% of the variation in the dependent variable is explained by the model.

Question 18

Which of the following is a correct statement about the standard error of a regression coefficient?

Accepted Answer

A smaller standard error indicates a more precise estimate.

Question 19

In a log-linear regression model, the coefficients $$b$$ and $$c$$ are interpreted as:

Accepted Answer

Elasticities.

Basic Estimation Techniques in Regression Analysis

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