# In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the

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Question 1 (2 points)

In choosing the “best-fitting” line through a set of points in linear regression, we choose the one with the:

Question 1 options:

smallest sum of squared residuals

largest sum of squared residuals

smallest number of outliers

largest number of points on the line

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Question 2 (2 points)

In linear regression, a dummy variable is used:

Question 2 options:

to represent residual variables

to represent missing data in each sample

to include hypothetical data in the regression equation

to include categorical variables in the regression equation

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Question 3 (4 points)

A multiple regression analysis included 4 independent variables results in sum of squares for regression of 1400 and sum of squares for error of 600. The multiple coefficient of determination will be:

Question 3 options:

.300

.700

.429

.084

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Question 4 (2 points)

A “fan” shape in a scatterplot indicates:

Question 4 options:

a nonlinear relationship

the absence of outliers

sampling error

unequal variance

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Question 5 (2 points)

In regression analysis, the variables used to help explain or predict the response variable are called the

Question 5 options:

independent variables

dependent variables

regression variables

statistical variables

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Question 6 (2 points)

A scatterplot that appears as a shapeless mass of data points indicates:

Question 6 options:

a curved relationship among the variables

a linear relationship among the variables

a nonlinear relationship among the variables

no relationship among the variables

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Question 7 (2 points)

The coefficient of determination ( ) can be interpreted as the fraction (or percent) of variation of the

Question 7 options:

explanatory variable explained by the independent variable

explanatory variable explained by the regression line

response variable explained by the regression line

error explained by the regression line

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Question 8 (2 points)

The correlation value ranges from

Question 8 options:

0 to +1

-1 to +1

-2 to +2

– to+

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Question 9 (2 points)

To help explain or predict the response variable in every regression study, we use one or more explanatory variables. These variables are also called predictor variables or independent variables.

Question 9 options:

True

False

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Question 10 (2 points)

When the scatterplot appears as a shapeless swarm of points, this can indicate that there is no relationship between the response variable Y and the explanatory variable X, at least none worth pursuing.

Question 10 options:

True

False

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Question 11 (2 points)

A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis) versus fitted values (on the horizontal axis), where a “good” fit not only has small residuals, but it has residuals scattered randomly around zero with no apparent pattern.

Question 11 options:

True

False

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Question 12 (2 points)

A negative relationship between an explanatory variable X and a response variable Y means that as X increases, Y decreases, and vice versa.

Question 12 options:

True

False

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Question 13 (4 points)

A regression analysis between weight (Y in pounds) and height (X in inches) resulted in the following least squares line: = 140 + 5X. This implies that if the height is increased by 1 inch, the weight is expected to increase on average by 5 pounds.

Question 13 options:

True

False

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Question 14 (4 points)

In regression analysis, if the coefficient of determination is 1.0, then the coefficient of correlation must be 1.0.

Question 14 options:

True

False

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Question 15 (4 points)

The residual is defined as the difference between the actual and fitted values of the response variable.

Question 15 options:

True

False

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Question 16 (4 points)

If the coefficient of correlation is -0.88, then the percentage of the variation in Y that is explained by the regression is 77.44%.

Question 16 options:

True

False

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Question 17 (4 points)

The coefficient of determination R2 is the square of the coefficient of correlation.

Question 17 options:

True

False

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Question 18 (4 points)

A regression analysis between sales (in $1000) and advertising (in $) resulted in the following least squares line: = 32 + 8X. This implies that an increase of $1 in advertising is expected to result in an increase of $40 in sales. BE CAREFUL!

Question 18 options:

True

False

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Question 19 (2 points)

A multiple regression model has the form . The coefficient b1 is interpreted as the change in Y per unit change in X1.

Question 19 options:

True

False

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Question 20 (4 points)

This question and the next two are based on the following information:

The maker of the Super B softball bat is interested in determining how certain factors affect the sales of its new model bat. The data below compares the number of bats (Y) that were sold, the average selling price (), and the disposable income per household () in the surrounding area at 10 large sporting goods stores that carry the Super Bbat. Simple regression was used to compare each independent variable to the number of bats sold. The regression output from Excel is shown below:

Is there evidence of a linear relationship between the number of bats sold and the average selling price of the bats? Support your response. If you believe there is a linear relationship, characterize the relationship (i.e., positive, negative, strong, weak, etc.).

Question 20 options:

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Question 21 (4 points)

Is there evidence of a linear relationship between the number of bats sold and disposable income in the area? Support your response If you believe there is a linear relationship, characterize the relationship (i.e., positive, negative, strong, weak, etc.).

Question 21 options:

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Question 22 (2 points)

Which of the two variables, the average selling price or the disposable income would you select for a simple linear regression model to predict the number of bats sold?

Question 22 options:

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Question 23 (3 points)

This question and the next seven are based on the following information:

The marketing manager of a large supermarket chain would like to determine the effect of shelf space (in feet) on the weekly sales of international food (in hundreds of dollars). A random sample of 12 equal –sized stores is selected, with the following results:

Below is a scatterplot for this data. Comment on the relationship between shelf space and weekly sales.

Question 23 options:

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Question 24 (5 points)

Use StatTools to obtain the indicated simple linear regression results for the data given in Question 23. The output (with blank cells A-E) is given below.

Provide the correct values for cells A, B, C, D, and E.

Question 24 options:

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Question 25 (2 points)

What is the least squares estimate of the Y-intercept?

Question 25 options:

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Question 26 (2 points)

What is the least squares estimate of the slope?

Question 26 options:

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Question 27 (2 points)

Interpret the meaning of the slope b.

Question 27 options:

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Question 28 (4 points)

Predict the average weekly sales (in hundreds of dollars) of international food for stores with 13 feet of shelf space for international food.

Question 28 options:

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Question 29 (4 points)

Would it be appropriate to predict the average weekly sales (in hundreds of dollars) of international food for stores with 35 feet of shelf space for international food? Why or why not?

Question 29 options:

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Question 30 (4 points)

State the value of the coefficient of determination, R2, and interpret its meaning.

Question 30 options:

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