Q: Given the regression equation $$\text{Estimated Production Time} = 172 + 2.44 \times \text{Number of Units}$$, what is the predicted production time for an order of 100 units?

$$172 + 2.44 \times 100 = 416$$

Question 1

Which of the following is NOT an assumption of the Simple Regression Model (SRM)?

Accepted Answer

Errors are uniformly distributed.

Question 2

Given the regression equation $$	ext{Estimated Production Time} = 172 + 2.44 	imes 	ext{Number of Units}$$, what is the predicted production time for an order of 100 units?

Accepted Answer

$$172 + 2.44 	imes 100 = 416$$

Question 3

In the SRM, the slope parameter $$\$$beta_1$$ represents:

Accepted Answer

The average change in $$Y$$ for a one-unit increase in $$X$$

Question 4

Which condition is checked by plotting the residuals versus the explanatory variable in the SRM?

Accepted Answer

Linearity of the association

Question 5

If the spread of residuals increases as $$X$$ increases, which SRM assumption is violated?

Accepted Answer

Equal variance of errors

Question 6

A company models monthly sales ($$Y) as a $$function of advertising spending ($$X) $$using $$\mu_{Y|X} = 500 + 2X. $$What is the interpretation of the number 500 in this equation?

Accepted Answer

It is the expected sales when advertising spending is zero.

Question 7

Which of the following would increase the estimated standard error of the slope $$b_1 in a $$regression model?

Accepted Answer

Increasing the standard deviation of the residuals

Question 8

What is the main difference between a confidence interval and a prediction interval in regression?

Accepted Answer

A confidence interval estimates a parameter; a prediction interval estimates the location of a new observation.

Question 9

Suppose you want to test $$H_0$$: \$$beta_1 = 0$ in a regression model. Which statistic would you use?

Accepted Answer

The t-statistic for the slope

Question 10

If the p-value for the slope in a regression model is less than 0.05, what does this imply?

Accepted Answer

There is statistically significant evidence that the slope is different from zero.

Question 11

Which of the following is a plausible lurking variable in a regression of production time on number of units?

Accepted Answer

Complexity of parts ordered

Question 12

A prediction interval for a new observation is reliable only if:

Accepted Answer

The SRM assumptions of constant variance and normality hold.

Question 13

Which of the following best describes the data generating process in the SRM?

Accepted Answer

At each value of $$X$$, the response $$Y is $$normally distributed around the regression line.

Question 14

In the SRM, what does $$E(\varepsilon) = 0$$ mean?

Accepted Answer

The average error is zero.

Question 15

Which of the following is NOT a step in the modeling process for SRM?

Accepted Answer

Ignore the quantile plot of the residuals.

Question 16

If zero lies outside the 95% confidence interval for the slope, what can you conclude?

Accepted Answer

The slope is significantly different from zero at the 5% significance level.

Question 17

Which of the following would make a prediction interval wider?

Accepted Answer

Increasing the standard deviation of the residuals

Question 18

Why is extrapolation problematic in regression analysis?

Accepted Answer

Prediction intervals may fail when the SRM does not hold outside the range of observed data.

Question 19

In a regression output, the t-statistic for the intercept is -7.68 with a p-value \u003c 0.0001. What does this indicate?

Accepted Answer

The intercept is significantly different from zero.

Question 20

Which of the following is a correct formula for the 95% confidence interval for the slope $$\$$beta_1$$?

Accepted Answer

$$b_1$$ \pm t^* 	imes SE($$b_1$$)$$

Chapter 21: The Simple Regression Model – Business Statistics Study Notes

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