Correlation Coefficient Analysis Using Technology

00:00 6 marks

A business analyst is investigating the relationship between advertisement spend and sales revenue. A dataset of paired values representing advertisement spend (in thousands of dollars) and sales revenue (in thousands of dollars) is collected. Using your Graphing Display Calculator (GDC), perform the following tasks:

Part a

4 minutes 2 marks

Question

Describe the step-by-step process to enter the provided paired data into your GDC to prepare for correlation analysis. Include checks to ensure data entry accuracy.

Hint Hint

Hint

Focus on the sequence of operations on the GDC, including accessing list functions, inputting data, and methods for verification.

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation
Formula Booklet

Answer Answer

Complete Answer

Data is correctly entered into the GDC’s lists, with one list for advertisement spend and another for sales. The process should include steps for data verification against the original dataset.

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Formula Booklet

Part b

6 minutes 4 marks

Question

Using your GDC, calculate the Pearson correlation coefficient (\(r\)) for the advertisement spend and sales revenue dataset. Interpret the calculated value of \(r\) in the context of the business scenario, commenting on the strength and direction of the linear relationship between advertisement spend and sales revenue.

Hint Hint

Hint

To calculate \(r\), use the linear regression function on your GDC. When interpreting, consider the scale of \(r\) (from -1 to +1) and what each end of the scale implies for the relationship between the variables in a business context.

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation
Formula Booklet

Answer Answer

Complete Answer

The computed Pearson correlation coefficient (\(r\)) is approximately 0.85. This indicates a strong positive linear relationship between advertisement spend and sales revenue, suggesting that as advertisement spend increases, sales revenue tends to increase significantly.

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Formula Booklet