Question

Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown to the right. Find and interpret value of R^2. What is the value of R^2? % (Round to two decimal places as needed.) What is the interpretation of R^2? The value of R^2 = % indicates the percentage of the variability in the of these disk drives that be explained by the variability in the of the drives. (Round to two decimal places as needed.)

Answer 1

R² represents the proportion of variance in a dependent variable explained by an independent variable in a regression model. If r is 0.6631, then R² is approximately 43.97%, implying that around 44% of the variability in disk drive prices is explained by their capacities.

Step-by-step explanation:

The coefficient of determination, denoted as R², is a statistic that indicates the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. The value of R² is the square of the correlation coefficient r, and it is generally expressed as a percentage. If the survey of prices for external disk drives resulted in a correlation coefficient r of 0.6631, as in the provided data example, the R² would be calculated as follows:

R² = (0.6631)² ≈ 0.4397

Expressed as a percentage, this R² would be 43.97%, which can be rounded to 44.00%. This indicates that 44.00% of the variability in the prices of these disk drives can be explained by the variability in their capacities.