Question 1

Which of the following best describes the relationship between fat and protein in the Burger King menu scatterplot (see $$image_1$$)?

Accepted Answer

There is a strong positive linear relationship.

Question 2

Which of the following is NOT a condition that must be checked before using correlation or regression?

Accepted Answer

Categorical Variables Condition

Question 3

Given the regression equation $$y = 220.89 - 7.775x$$ for mortgages (in billions of dollars) versus interest rate, what does the slope represent?

Accepted Answer

For each 1% increase in interest rate, the average mortgage amount decreases by 7.775 billion dollars.

Question 4

What is a residual in the context of linear regression?

Accepted Answer

The difference between the observed y and the predicted y.

Question 5

Why do we square the residuals when finding the least squares regression line?

Accepted Answer

To give more weight to larger errors and avoid cancellation of positive and negative values.

Question 6

Which variable should be the explanatory (predictor) variable in a regression of house selling price and square footage?

Accepted Answer

Square footage

Question 7

If the $$R^2$$ value for a regression model is 0.5743, how should this be interpreted?

Accepted Answer

57.43% of the variation in the response variable is explained by the model.

Question 8

Which of the following is a sign that a linear regression model may NOT be appropriate for your data?

Accepted Answer

The residual plot shows a clear pattern or curve.

Question 9

What does it mean if the p-value for the slope in a regression output is greater than 0.05?

Accepted Answer

There is not enough evidence to conclude a linear relationship exists.

Question 10

Which of the following is a potential problem when using a regression equation to make predictions for values of x outside the range of the original data?

Accepted Answer

The predictions may be unreliable due to extrapolation.

Question 11

Suppose the regression equation for hurricane wind speed (y) and central pressure (x) is $$y = 1031.24 - 0.975x. $$What does the slope mean in this context?

Accepted Answer

For each 1 mb increase in central pressure, the maximum wind speed decreases by 0.975 knots.

Question 12

Which of the following is NOT a correct interpretation of the y-intercept in a regression equation?

Accepted Answer

It always has a meaningful real-world interpretation.

Question 13

If the correlation coefficient $$r is 0.7578$$, what is the value of $$R^2$$?

Accepted Answer

$$R^2 = 0.5743$

Question 14

Which of the following best describes the purpose of examining residual plots in regression analysis?

Accepted Answer

To assess whether the assumptions of the regression model are met.

Question 15

A regression analysis between SAT score (x) and college GPA (y) yields a statistically significant slope. What does this mean?

Accepted Answer

There is evidence of a linear relationship between SAT score and college GPA.

Question 16

Which of the following is a correct statement about the roles of variables in regression?

Accepted Answer

The explanatory variable is plotted on the x-axis.

Question 17

If the standard deviation of the residuals ($$s_e) is $$much smaller than the standard deviation of y ($$s_y$$), what does this indicate about the regression model?

Accepted Answer

The model explains a large proportion of the variation in y.

Question 18

Which of the following is a reason to report the $$R^2$$ value when presenting a regression model?

Accepted Answer

It shows the proportion of variance in the response variable explained by the model.

Linear Regression: Concepts, Interpretation, and Statistical Significance

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