An industry analyst tracks weekly box office revenues for a film over 20 weeks and wants to know if there is a linear relationship between sales and time. Which inference method would be appropriate?

An industry analyst tracks weekly box office revenues for a film over 20 weeks and wants to know if there is a linear relationship between sales and time. Which inference method would be appropriate?

• A. Pearson correlation
• B. ANOVA
• C. Linear regression t-test (degrees of freedom unknown)
• D. Paired t-test

Answer: (C)

Fitting a simple linear regression is the way to go when you want to know if time and box office revenue relate in a linear way. You use time as the predictor and revenue as the response, estimate the line, and then test whether the slope is different from zero. The slope tells you how much revenue changes per week, so a statistically significant slope means there’s a linear relationship between time and sales. This approach gives you both the equation of the line and a formal test of whether time has a meaningful linear effect. Pearson correlation only measures how strong the linear relationship is and doesn’t directly provide a regression model or a test of whether the slope is nonzero. ANOVA is about comparing means across groups, not about a single continuous predictor. A paired t-test is for comparing two related samples, which isn’t the situation here.

Fitting a simple linear regression is the way to go when you want to know if time and box office revenue relate in a linear way. You use time as the predictor and revenue as the response, estimate the line, and then test whether the slope is different from zero. The slope tells you how much revenue changes per week, so a statistically significant slope means there’s a linear relationship between time and sales. This approach gives you both the equation of the line and a formal test of whether time has a meaningful linear effect.

Pearson correlation only measures how strong the linear relationship is and doesn’t directly provide a regression model or a test of whether the slope is nonzero. ANOVA is about comparing means across groups, not about a single continuous predictor. A paired t-test is for comparing two related samples, which isn’t the situation here.