Question 1

Which of the following best describes the purpose of simple linear regression in business statistics?

Accepted Answer

To predict the value of a dependent variable based on the value of an independent variable.

Question 2

Given the regression equation $$\hat{y} = b_0$ + b_1$ x$$, what does $$b_1$$ represent in the context of a real estate pricing model where $$x is $$square footage and $$y is $$house price?

Accepted Answer

$$b_1 is $$the estimated change in average house price for each additional square foot.

Question 3

Which of the following is NOT an assumption of the simple linear regression model?

Accepted Answer

The error terms are correlated with each other.

Question 4

Suppose a regression analysis yields $$R^2 = 0.80$. What does this indicate about the model?

Accepted Answer

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

Question 5

Given the following regression output for predicting house price ($$y) $$from square footage ($$x$$): $$\hat{y} = 98.25 + 0.1098x. $$What is the predicted price for a house with 2,000 square feet?

Accepted Answer

$317,850

Question 6

Which formula correctly calculates the slope coefficient $$b_1 in a $$simple linear regression?

Accepted Answer

$$b_1$$ = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^n (x_i - \bar{x}$$)^2$$}$$

Question 7

A business analyst wants to test if the independent variable in a regression is significant. Which hypothesis test should they use?

Accepted Answer

A t-test for the slope coefficient ($$b_1)$$

Question 8

If the sum of squared errors (SSE) is large relative to the total sum of squares (SST), what can you conclude about the regression model?

Accepted Answer

The model explains little of the variation in the dependent variable.

Question 9

Which of the following best describes the difference between a confidence interval for the mean response and a prediction interval for an individual response in regression?

Accepted Answer

The prediction interval is wider because it accounts for both the error in estimating the mean and the variability of individual outcomes.

Question 10

A company regresses its stock returns on the market index returns and obtains a slope coefficient of 1.2. What does this Beta coefficient indicate?

Accepted Answer

The company's stock is more volatile than the market.

Question 11

Which formula gives the coefficient of determination, $$R^2$$, in terms of sums of squares?

Accepted Answer

$$R^2$$ = \frac{SSR}{SST}$$

Question 12

Which of the following is a correct interpretation of a regression intercept ($$b_0) in a $$business context?

Accepted Answer

It is the estimated average value of the dependent variable when the independent variable is zero, if zero is within the range of observed values.

Question 13

A regression analysis yields a sample correlation coefficient $$r = 0.7. $$What is the value of $$R^2$$?

Accepted Answer

$$0.49$$

Question 14

Which of the following is the correct formula for the standard error of the estimate, $$s_e$$?

Accepted Answer

$$s_e = \sqrt{\frac{SSE}{n-2}}$$

Question 15

Which of the following statements about correlation is TRUE?

Accepted Answer

Correlation measures the strength of a linear relationship but does not imply causation.

Question 16

A regression model is used to predict sales based on advertising spending. The analyst wants to test if advertising spending has a significant effect on sales. Which null hypothesis should be tested?

Accepted Answer

$$H_0$$: \$$beta_1 = 0$

Question 17

Which of the following is a potential problem in regression analysis that can be detected using graphical analysis?

Accepted Answer

Presence of outliers that strongly influence the regression line.

Question 18

If you use a regression model to predict values far outside the range of your observed data, what is this practice called and why is it risky?

Accepted Answer

Extrapolation; because the relationship may not hold outside the observed range.

Question 19

Which formula is used to test the null hypothesis that the population correlation coefficient is zero?

Accepted Answer

$$t = \frac{r \sqrt{n-2}}{\sqrt{1 - r^2$}}$$

Simple Linear Regression: Concepts, Computation, and Interpretation

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