Free Practice Quiz Question List

11 Simple Linear Regression Online Quiz Questions

Use this free practice quiz with 20 questions to review 11 Simple Linear Regression, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

For the fitted equation $\hat y=52+4.5x$ , what is the correct interpretation of the slope?

A
The predicted score is 52 points for every student.
B
The predicted score increases by 4.5 points for each additional hour studied, on average.
C
The actual score increases by exactly 4.5 points for every additional hour studied.
D
Studying for 4.5 hours causes the score to increase by 52 points.

Fill in the blank

1 point

The standard simple linear regression assumptions are commonly summarized by the acronym .

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1 point

A fitted regression model has $R^2=0.64$ . Which interpretation is supported by the material?

A
The predictor causes 64% of the response values.
B
The fitted model explains 64% of the observed sample variation in the response.
C
The model predicts every response with 64% accuracy.
D
The slope must equal 0.64.

Fill in the blank

1 point

In the formula $R^2=1-\frac{SSE}{SST}$ , $SST$ represents the in the response.

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1 point

Which statements correctly describe a prediction interval for a new individual response in simple linear regression? Select all that apply.

A
It estimates the response for one new individual or unit at a specified predictor value.
B
It estimates only the mean response for all units at a specified predictor value.
C
It includes individual-to-individual random variation around the mean response.
D
It is generally most precise when the predictor value is far outside the observed range.

Written response

1 point

A fitted line is $\hat y=18+3x$ . For an observation with $x=10$ and observed response $y=50$ , enter the residual in score points. The residual is observed minus fitted.

Choose one

1 point

A 95% confidence interval for a population slope is $(2.1,6.9)$ . Which conclusion is justified?

A
The population slope is exactly 4.5.
B
The data are consistent with a positive population slope.
C
The fitted model proves that the predictor causes the response to increase.
D
The population slope must be outside the interval in 5% of individual observations.

Written response

1 point

For the fitted equation $\hat y=10+2.5x$ , what is the predicted response when $x=12$ ?

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1 point

Which property defines the least-squares regression line?

A
It has the smallest possible sum of squared residuals among straight lines.
B
It necessarily gives a causal explanation of the response.
C
It always has an intercept that is meaningful at $x=0$ .
D
It produces zero residuals for every observation.

Choose all

1 point

Which statements correctly describe ways to diagnose simple linear regression assumptions? Select all that apply.

A
A curved residual pattern can suggest nonlinearity.
B
A funnel-shaped residual pattern can suggest unequal variance.
C
A random horizontal band proves that the study is randomized.
D
A pattern by observation order or time can suggest dependence.

Open ended

1 point

Explain the difference between a confidence interval for the population slope and a prediction interval for one new individual response. Why is the prediction interval wider, and what causal conclusion can be drawn from either interval alone?

Choose one

1 point

Which expression correctly defines the residual for an observation in a simple linear regression model?

A
The fitted response minus the observed response
B
The observed response minus the fitted response
C
The predictor value minus the response value
D
The squared difference between the observed and fitted responses

Choose one

1 point

A fitted regression equation is $\hat y=18+2.7x$ , where $x$ is measured in hours and $y$ is measured in points. Which interpretation of the slope is correct?

A
The predicted value of the predictor when the response increases by one unit
B
The response value when the predictor is zero, regardless of whether zero is meaningful
C
The estimated change in predicted response for a one-unit increase in the predictor
D
The proportion of response variation explained by the predictor

True or false

1 point

True or false: A statistically strong linear association in a regression model automatically proves that changes in the predictor cause changes in the response.

A
True
B
False

Written response

1 point

A regression model predicts an exam score of $79$ for a student, whose actual score is $84$ . What is the residual, in score points?

Choose one

1 point

A simple linear regression has $R^2=0.64$ . Which interpretation is appropriate?

A
Sixty-four percent of the observed sample variation in the response is explained by the fitted linear model.
B
The predictor causes 64% of every individual response.
C
The fitted model predicts 64% of individual responses exactly.
D
The slope of the fitted line is 0.64 response units per predictor unit.

Written response

1 point

A simple linear regression is based on $n=18$ paired observations. What degrees of freedom should be used for the $t$ -test of the population slope?

Choose one

1 point

Why is a prediction interval for one new individual response generally wider than a confidence interval for the mean response at the same predictor value?

A
It estimates the population slope rather than a response.
B
It is narrower because it excludes individual random variation.
C
It applies only when the predictor value is outside the observed range.
D
It is wider because it includes individual-to-individual variation as well as uncertainty in the estimated mean.

True or false

1 point

True or false: The least-squares regression line always passes through $(\bar x,\bar y)$ , the point formed by the sample means of the predictor and response.

A
True
B
False

True or false

1 point

True or false: If a fitted regression equation has intercept $18$ , the value $18$ should always be interpreted as the predicted response when $x=0$ , regardless of whether $x=0$ is meaningful or within the observed range.

A
True
B
False