Disk drives have been getting larger. Their capacity is now often given in terabytes​ (TB) where 1 TBequals
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 Rsquared
.
	
Capacity​ (in TB)
	
Price​ (in $)
	
 
	
0.080
21.00
	
0.120
26.45
	
0.300
45.45
	
0.360
57.55
	
1.0
119.45
	
2.0
246.99
	
4.0
393.00
Question content area bottom
Part 1
What is the value of Upper R squared
​?

To find the value of $ R^2 $ (coefficient of determination), we need to perform a linear regression analysis. The value of $ R^2 $ tells us how well the regression line fits the data, and it represents the proportion of the variance in the dependent variable (Price) that can be explained by the independent variable (Capacity in TB).

Given the dataTo find the value of $ R^2 $ (coefficient of determination), we need to perform a linear regression analysis. The value of $ R^2 $ tells us how well the regression line fits the data, and it represents the proportion of the variance in the dependent variable (Price) that can be explained by the independent variable (Capacity in TB).

Given the 
- Capacity (TB): $ 0.080, 0.120, 0.300, 0.360, 1.0, 2.0, 4.0 $
- Price ($): $ 21.00, 26.45, 45.45, 57.55, 119.45, 246.99, 393.00 $

We will calculate the regression line and then determine the value of $ R^2 $. I'll proceed with these calculations now.The value of $ R^2 $ is approximately $ 0.988 $. 

### Interpretation:
This means that about 98.8% of the variance in the price of disk drives can be explained by their capacity (in terabytes) using the linear regression model. This indicates a very strong linear relationship between the capacity and the price of the disk drives.

Would you like more details on how this value was calculated or how to interpret it?

Here are some related questions:
1. What does an $ R^2 $ value close to 1 indicate in a regression analysis?
2. How do outliers affect the value of $ R^2 $?
3. What are the limitations of using $ R^2 $ as a measure of model fit?
4. How can we determine if a linear model is the best fit for this data?
5. What other metrics can we use to evaluate the performance of a regression model?

**Tip:** An $ R^2 $ value above 0.9 generally suggests a strong correlation, but always check for overfitting, especially with small datasets.

Disk drives have been getting larger. Their capacity is now often given in terabytes​ (TB) where 1 TB equals 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 the value of R-squared.

Learn how to calculate the R-squared value for the relationship between the capacity (in terabytes) and price of disk drives using linear regression. This problem covers key statistical concepts like the coefficient of determination (R^2) and the least squares method. Suitable for students in Grades 11-12.

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