Correlation; Pearson's r; regression y on x practice questions.

For a bivariate data set, Pearson's correlation coefficient is r = -0.92. Which description of the relationship between the variables is correct?

• Strong positive linear correlation
• Weak negative linear correlation
• No linear correlation
• Strong negative linear correlation

Answer: Strong negative linear correlation

The sign of r gives the direction (negative) and |r| close to 1 indicates a strong linear relationship, so r = -0.92 is a strong negative linear correlation.

The regression line of exam score y on hours studied x is y = 3.2x + 5.1. What is the correct interpretation of the value 3.2?

• The expected score of a student who studies for 0 hours
• The number of hours needed to obtain a score of 5.1
• On average, the score rises 3.2 points per extra hour studied
• The score increases by 5.1 points for each additional hour studied

Answer: On average, the score rises 3.2 points per extra hour studied

The gradient of the regression line gives the average change in y per unit increase in x; the intercept 5.1 is the predicted score at x = 0.

Which of the following is NOT a possible value of Pearson's correlation coefficient r?

• -0.99
• 1.2
• 0
• 0.85

Answer: 1.2

Pearson's r always satisfies -1 ≤ r ≤ 1, so a value of 1.2 is impossible.

Which point must always lie on the regression line of y on x?

• (x̄, ȳ)
• (0, ȳ)
• (x̄, 0)
• (mode of x, mode of y)

Answer: (x̄, ȳ)

By construction, the least-squares regression line of y on x passes through the mean point (x̄, ȳ). This fact is often used to find the equation of the line.

A study finds a strong positive correlation between daily ice cream sales and the number of swimming accidents in a city. Which conclusion is most justified?

• Buying ice cream causes swimming accidents
• Swimming accidents cause people to buy ice cream
• A third variable (hot weather) may explain it
• The correlation must be a calculation error

Answer: A third variable (hot weather) may explain it

Correlation does not imply causation: a confounding variable (temperature) can drive both quantities, producing the observed association.

The regression line of y on x is y = 2.5x - 4. Calculate the predicted value of y when x = 8.

• 24
• 4.8
• -4
• 16

Answer: 16

Substituting x = 8 gives y = 2.5 × 8 - 4 = 20 - 4 = 16. A common error is adding 4 instead of subtracting.