Question 1

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

Accepted Answer

It minimizes the sum of the squared residuals.

Question 2

Given the regression equation $$\$$ \hat{y} = 8.4 + 0.91x \$$\$$, where $$\ x$$ \$$\ is $$protein content in grams and $$\$$ \hat{y} \$$\ is $$fat content in grams, what does the slope of 0.91 represent?

Accepted Answer

For each additional gram of protein, fat content increases by 0.91 grams.

Question 3

A residual in regression analysis is defined as:

Accepted Answer

The observed value minus the predicted value.

Question 4

If a data point lies above the regression line, what can be said about its residual?

Accepted Answer

The residual is positive.

Question 5

Suppose the correlation coefficient $$\ r$$ \$$\$$ between protein and fat content in Burger King menu items is 0.76. What percentage of the variation in fat content is explained by the linear model?

Accepted Answer

$$\ 58$$\% \$$\$$

Question 6

Given the regression equation $$\$$ \hat{y} = 6.18 - 0.0196x \$$\$$, where $$\ x$$ \$$\ is $$the age of a bridge and $$\$$ \hat{y} \$$\ is $$its safety score, what does the slope indicate?

Accepted Answer

Safety score decreases by 0.0196 points per year of age.

Question 7

Which of the following is NOT a condition that must be checked before using a regression model for prediction?

Accepted Answer

The sample size must be greater than 100.

Question 8

If the correlation coefficient $$\ r$$ \$$\ is $$negative, what does this imply about the relationship between the two variables?

Accepted Answer

As one variable increases, the other decreases.

Question 9

Why is it incorrect to simply switch $$\ x$$ \$$\$$ and $$\ y$$ \$$\ in $$the regression equation to predict $$\ x$$ \$$\$$ from $$\ y$$ \$$\$$?

Accepted Answer

Because switching $$\ x$$ \$$\$$ and $$\ y$$ \$$\$$ requires recalculating the regression parameters from scratch.

Question 10

A regression model for hurricane wind speed versus central pressure yields $$\$$ $$R^2 = 0.806$$ \$$\. $$What does this value mean?

Accepted Answer

80.6% of the variability in wind speed is explained by central pressure.

Question 11

Which of the following statements about regression and causation is correct?

Accepted Answer

Regression analysis alone can never establish causation.

Question 12

In the context of regression, what does 'regression to the mean' refer to?

Accepted Answer

Predicted values tend to be closer to the mean than the observed values.

Question 13

Suppose you use the regression equation $$\$$ \hat{y} = 8.4 + 0.91x \$$\ to $$predict the fat content of a Burger King item with 31g of protein. The actual fat content is 22g. What is the residual?

Accepted Answer

$$\ 22 - (8.4 + 0.91$$ 	imes 31) = -14.7 \$$\$$

Question 14

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

Accepted Answer

The scatterplot of residuals shows bends or curves.

Question 15

The standard deviation of the residuals in a regression model is best interpreted as:

Accepted Answer

A measure of how well the regression line fits the data.

Question 16

In a regression analysis of calories versus sugar content in breakfast cereals, the regression equation is $$\$$ \hat{y} = 89.6 + 2.49x \$$\$$, where $$\ x$$ \$$\ is $$sugar in grams. What is the predicted calorie content for a cereal with 10g of sugar?

Accepted Answer

$$\ 89.6 + 2.49$$ 	imes 10 = 114.9 \$$\$$

Question 17

Which of the following is true about the correlation coefficient $$\ r$$ \$$\$$ and the slope $$\$$ $$b_1$$ \$$\ in a $$regression model?

Accepted Answer

They always have the same sign.

Question 18

Which of the following is NOT a recommended practice when reporting regression results?

Accepted Answer

Claim that a high $$\$$ $$R^2$$ \$$\$$ proves causation.

Linear Regression: Least Squares and the Line of Best Fit

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