$$\text{Estimated Cost} = 15.20 + 2697.25 \times \text{Weight}$$

Question 1

Which equation best represents the least squares regression line for predicting diamond price from weight, based on the provided parameter estimates?

Accepted Answer

$$	ext{Estimated Cost} = 15.20 + 2697.25 	imes 	ext{Weight}$$

Question 2

If a diamond weighs 0.4 carats, what is its estimated price using the regression equation $$	ext{Estimated Cost} = 15 + 2697 	imes 	ext{Weight}$$?

Accepted Answer

$$1,093.80$$

Question 3

What does the slope ($$b_1) in $$the regression equation for diamond price represent?

Accepted Answer

The estimated marginal cost per carat of diamond weight

Question 4

Which of the following best describes a residual in regression analysis?

Accepted Answer

The vertical deviation of a data point from the fitted regression line

Question 5

If the standard deviation of residuals ($$s_e) is$$ $$145$$, what does this value indicate about the regression model?

Accepted Answer

On average, the actual prices deviate from the fitted line by about $$145$$

Question 6

What is the interpretation of the intercept ($$b_0) in $$the regression equation for diamond price?

Accepted Answer

The estimated price when the diamond weight is zero

Question 7

Which condition must be checked to ensure the appropriateness of simple linear regression?

Accepted Answer

The residuals should show random variation with no clear pattern

Question 8

What does $$R^2$$ represent in the context of regression analysis?

Accepted Answer

The fraction of variation in the response variable explained by the regression line

Question 9

If $$R^2$$ \approx 0.5$$ for the diamond price regression, what does this imply?

Accepted Answer

About 50% of the variation in diamond price is explained by weight

Question 10

A diamond weighs 0.5 carats. Using the regression equation $$	ext{Estimated Cost} = 15 + 2697 	imes 	ext{Weight}$$, what is the estimated price?

Accepted Answer

$$1,363.50$$

Question 11

Which of the following is NOT a condition for simple regression?

Accepted Answer

The response variable must be categorical

Question 12

What is the main purpose of plotting residuals against the predictor variable?

Accepted Answer

To check for patterns that might indicate model inadequacy

Question 13

If the residual plot shows a clear pattern, what does this suggest about the regression model?

Accepted Answer

The model may not adequately capture the relationship between variables

Question 14

Which formula is used to calculate the residual for a data point in regression?

Accepted Answer

$$e_i = y_i - (b_0$ + b_1$ x_i)$$

Question 15

Why is it important to report both $$R^2$$ and $$s_e$$ when summarizing a regression model?

Accepted Answer

They together describe how well the regression equation fits the data

Question 16

In the diamond price example, what is the average increase in price when weight increases from 0.4 to 0.5 carats?

Accepted Answer

$$269.70$$

Question 17

Which of the following statements about the slope in regression is correct?

Accepted Answer

It estimates the marginal change in the response variable per unit increase in the predictor

Question 18

What is the empirical rule implication for the standard deviation of residuals in the diamond price regression?

Accepted Answer

About 95% of prices are within $$290 of $$the regression line

Question 19

Which of the following is a plausible lurking variable in the diamond price regression?

Accepted Answer

Diamond clarity or color

Ch . 19 Linear Patterns and Simple Regression: Study Notes for Business Statistics

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