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Module 11 Quiz: Simple Linear Regression

Test your understanding with 15 auto-graded questions

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Quiz Instructions

15 multiple choice questions covering all Module 11 content
Passing score: 70% (11 out of 15 correct)
Immediate feedback - see results as soon as you submit
Detailed explanations provided for each question
You may use a calculator, but show your work on paper
Take your time and read each question carefully

If r = -0.85, which statement is true?

There is a weak negative linear relationship

There is a strong negative linear relationship

There is a strong positive linear relationship

x causes y to decrease

The regression equation is ŷ = 100 - 5x. What does the -5 represent?

The y-intercept

The slope: y decreases by 5 for each 1-unit increase in x

The correlation coefficient

The predicted value when x = 0

If r² = 0.64, what does this mean?

The correlation coefficient r = 0.64

64% of the variation in y is explained by x

There is a 64% chance the variables are related

The slope equals 0.64

Using ŷ = 50 + 3x, predict y when x = 10.

500

A point has actual value y = 75 and predicted value ŷ = 70. What is the residual?

-5

145

Cannot be determined

Which condition is violated if a residual plot shows a clear U-shaped curve?

Linearity

Independence

Normality

Equal variance

When testing H₀: ρ = 0, what are we testing?

Whether the sample correlation equals zero

Whether there is a significant linear relationship in the population

Whether x and y are identical

Whether the y-intercept is zero

Testing H₀: ρ = 0 and H₀: β₁ = 0 with the same data will:

Give different conclusions

Give the same conclusion (they're equivalent tests)

Cannot both be performed on the same data

Use different sample sizes

Calculate the test statistic: n = 20, r = 0.50, testing H₀: ρ = 0

Use: t = r√[(n-2)/(1-r²)]

t = 2.00

t = 2.45

t = 3.16

t = 1.50

A 95% CI for slope is (2.5, 8.3). Can we reject H₀: β₁ = 0 at α = 0.05?

Yes, because the interval doesn't contain 0

No, because the interval doesn't contain 0

Cannot determine from a confidence interval

Yes, because both bounds are positive

Which correlation represents the strongest relationship?

r = 0.60

r = -0.85

r = 0.20

r = -0.50

What is the main difference between a confidence interval and a prediction interval?

They use different confidence levels

CI estimates a mean; PI predicts an individual value

They are the same thing

CI is wider than PI

Why is a prediction interval wider than a confidence interval for the same x value?

It uses a larger critical value

It accounts for individual variation (the "1 +" in the SE formula)

It has more degrees of freedom

It's based on a different regression equation

Ice cream sales and drowning deaths are positively correlated. This means:

Ice cream causes drowning

Drowning causes people to buy ice cream

Both increase in summer (confounding variable)

There is no relationship

The data ranges from x = 5 to x = 25. Predicting at x = 30 is an example of:

Interpolation (safe)

Extrapolation (risky)

A valid prediction

Testing the slope

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