A data analyst is investigating the relationship between advertising spend and sales revenue for a company over the past four quarters. The data is presented in a scatter plot where the x-axis represents 'Advertising Spend ($ thousands)' and the y-axis represents 'Sales Revenue ($ millions)'. A linear trend line has been fitted to the data. **Statement 1:** The equation of the linear trend line is y = 0.5x + 10, where y is Sales Revenue ($ millions) and x is Advertising Spend ($ thousands). **Statement 2:** The correlation coefficient (R-squared) for the trend line is 0.85. If the company increases its advertising spend by $20,000, can the analyst determine the expected increase in sales revenue?
- AEach statement alone is sufficient.
- BStatement 1 alone is sufficient, but statement 2 alone is not sufficient.
- CBoth statements together are sufficient, but neither statement alone is sufficient.
- DStatement 2 alone is sufficient, but statement 1 alone is not sufficient.
Show answer & explanationAnswer & explanation
Correct answer: B. Statement 1 alone is sufficient, but statement 2 alone is not sufficient.
Statement 1 provides the linear equation (y = 0.5x + 10) which directly relates advertising spend (x) to sales revenue (y). An increase in x by $20,000 (which is 20 in thousands) can be plugged into the slope (0.5) to find the change in y. Statement 2 only indicates the strength of the linear relationship but does not provide the specific functional form (slope) needed to calculate the expected change in sales.
Why the other options are wrong
- A. Statement 2 alone is not sufficient. This option is incorrect.
- C. Statement 1 alone is sufficient. Statement 2 is not necessary for this prediction. This option is incorrect.
- D. Statement 2 only gives R-squared, which indicates how well the model fits the data, but not the actual relationship (slope) to predict the change in sales. This option is incorrect.
Data Sufficiency: Linear Regression
Data Sufficiency questions involving linear regression models typically test whether the equation of the line (slope and intercept) is provided or can be derived to make predictions.
- Linear equation: y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.
- R-squared measures how well the model fits the data, but doesn't give the prediction formula itself.
- To predict a change in 'y' given a change in 'x', the slope 'm' is crucial.
Memory trick: To predict, you need the 'rules' of the relationship, not just how strong it is.