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Module 11: Pre-Assessment

Simple Linear Regression - Baseline Knowledge Check

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Instructions

Purpose: This pre-assessment measures your baseline knowledge before starting Module 11. Your answers help us understand your starting point and measure learning gains.

Guidelines:

5 questions covering simple linear regression concepts
No time limit - take your time
Do your best - it's okay if you don't know the answers yet!
No penalty - this does not affect your grade
Honest effort - answer based on your current knowledge (don't look up answers)

Research Note: Your responses are used to measure learning gains from pre- to post-assessment. This helps us improve the course and contributes to educational research.

Correlation Coefficient Interpretation

A researcher calculates the correlation coefficient between hours of study and exam scores and finds r = 0.85. What does this value tell us?

a) There is a strong positive linear relationship between study hours and exam scores

b) There is a weak positive linear relationship between study hours and exam scores

c) Studying more hours causes higher exam scores

d) 85% of the variation in exam scores is explained by study hours

Regression Equation

The regression equation for predicting weight (in pounds) from height (in inches) is: ŷ = -100 + 3.5x. What does the slope (3.5) represent?

a) The predicted weight when height is 0 inches

b) For each 1-inch increase in height, weight increases by 3.5 pounds on average

c) The correlation between height and weight is 3.5

d) The average weight in the dataset is 3.5 pounds

Coefficient of Determination

If r² = 0.64 for a regression analysis, which statement is correct?

a) The correlation coefficient r = 0.32

b) 64% of the variation in the response variable is explained by the explanatory variable

c) There is a 64% chance that the variables are related

d) The slope of the regression line is 0.64

Hypothesis Testing for Slope

When testing H₀: β₁ = 0 vs Hₐ: β₁ ≠ 0, what are we really testing?

a) Whether the y-intercept equals zero

b) Whether there is a significant linear relationship between x and y

c) Whether x and y have the same mean

d) Whether the correlation equals 1

Confidence vs Prediction Intervals

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

a) They use different critical values from the t-distribution

b) A confidence interval estimates the average y value; a prediction interval estimates a single y value

c) A prediction interval is always narrower than a confidence interval

d) They are the same thing with different names

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