Free Practice Quiz Question List

7 Correlation and Regression Online Quiz Questions

Use this free practice quiz with 20 questions to review 7 Correlation and Regression, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

A strong positive correlation between advertising spending and sales, by itself, establishes that increasing advertising causes sales to rise.

A
True
B
False

Choose one

1 point

A scatterplot shows a curved pattern between two quantitative variables, but Pearson’s correlation is near zero. Which interpretation is most appropriate?

A
There is no relationship of any kind between the variables.
B
There is little linear association, although a curved relationship may still exist.
C
There is a strong negative linear relationship.
D
One variable must cause the other to change.

Fill in the blank

1 point

A residual is the minus the .

Written response

1 point

A retailer uses a regression model to predict sales at an advertising-spending value beyond all values in the data used to fit the model. What is this kind of prediction called?

Choose one

1 point

What quantity does the least-squares method minimize when fitting a regression line?

A
The sum of the residuals.
B
The largest residual.
C
The sum of squared residuals.
D
The sum of squared predicted values.

Fill in the blank

1 point

At a given value of the explanatory variable, a confidence interval describes uncertainty about the , while a prediction interval describes an individual .

True or false

1 point

At the same explanatory-variable value, a prediction interval for an individual future outcome is wider than a confidence interval for the mean response because it also accounts for individual variation.

A
True
B
False

Choose all

1 point

A retailer is checking whether a straight-line regression model is suitable by examining its residual plot. Which features support a suitable straight-line model? Select all that apply.

A
Residuals are scattered around zero without a systematic curve.
B
Residuals form a clear curved pattern.
C
The spread of residuals stays roughly constant across fitted values.
D
The residuals’ spread steadily widens as fitted values increase.

Choose all

1 point

Which conditions are typically among the assumptions for inference about regression coefficients and conventional uncertainty estimates? Select all that apply.

A
A suitable linear form.
B
Independent errors.
C
A high coefficient of determination in every case.
D
Roughly constant error variance.
E
Approximately normal errors, especially for small-sample tests and intervals.
F
Proof that the explanatory variable causes the response.

Open ended

1 point

A retailer has used a regression model to forecast next month’s sales for an advertising budget within the range of the data used to fit the model. Before relying on the forecast to decide whether the budget is worthwhile, what should the retailer do to assess predictive performance and make a responsible decision?

Choose one

1 point

A scatterplot shows points clustered closely around a line that slopes downward from left to right. Which description best fits the relationship?

A
A weak positive linear correlation
B
A strong negative linear correlation
C
A strong positive linear correlation
D
No linear association, because the points trend downward

Choose one

1 point

When fitting a regression line by least squares, which quantity is minimized?

A
The sum of the observed response values
B
The number of data points above the fitted line
C
The sum of the squared differences between observed and predicted response values
D
The difference between the largest and smallest explanatory values

Written response

1 point

A retailer uses the model $\widehat{y}=20+4x$ , where advertising spending $x$ and predicted weekly sales $\widehat{y}$ are both measured in thousands of dollars. What weekly sales value does the model predict when advertising spending is 6 thousand dollars?

Choose one

1 point

A retailer models weekly sales (in thousands of dollars) from advertising spending (in thousands of dollars) using $\widehat{y}=20+4x$ . Which interpretation of the slope is appropriate?

A
Each additional $1,000 in advertising is associated with an estimated $4,000 increase in weekly sales, within the data's range and context.
B
Each additional $1,000 in weekly sales causes advertising spending to increase by $4,000.
C
Weekly sales are predicted to be $4,000 whenever advertising spending is zero.
D
Each additional $1,000 in advertising is associated with an estimated $4 increase in weekly sales.

Choose one

1 point

A residual plot shows residuals scattered around zero, but their vertical spread steadily widens as the predicted values increase. What potential issue does this pattern suggest?

A
The fitted model necessarily explains all variation in the response
B
The response has no relationship with the explanatory variable
C
The errors are necessarily independent
D
The error variance may not be constant

Written response

1 point

A regression model is used to predict an outcome at an explanatory-variable value higher than every value observed in the data used to fit the model. What is this practice called?

Choose one

1 point

At the same value of $x$ , why is a prediction interval for an individual future outcome generally wider than a confidence interval for the mean response?

A
A confidence interval for the mean response is wider because it includes individual variation.
B
A prediction interval for an individual future outcome is wider because it includes individual variation as well as uncertainty about the mean.
C
The intervals have the same width because both use the same fitted line.
D
A prediction interval describes only uncertainty about the average response.

Choose one

1 point

A retailer wants to check how well a fitted regression model predicts sales beyond the data used to estimate its line. Which approach is most appropriate when suitable data are available?

A
Refit and assess the model only on the same data, because that guarantees an unbiased performance check.
B
Keep the model only if its R² is high, regardless of how it performs on other data.
C
Compare predictions with outcomes in data not used to fit the model, such as a holdout sample.
D
Extrapolate beyond the observed range to test whether the line continues indefinitely.

True or false

1 point

A retailer fits a regression model using advertising values that do not include zero. The model's intercept still represents its predicted sales at zero advertising, but that interpretation may not be practically supported by the data. True or false?

A
True
B
False

Written response

1 point

A fitted model has R² = 0.72. What percentage of the observed variation in the response around its sample mean does the model account for? Enter the percentage, not a decimal.