To find the value of $R^2$ (coefficient of determination), we need to perform a linear regression analysis on the given data. This involves fitting a regression model and calculating $R^2$, which measures how well the independent variable (Capacity in TB) explains the dependent variable (Price in $).

Let's compute $R^2$ using regression analysis. numpy as np import statsmodels.api as sm

Given data

capacity_TB = np.array([0.080, 0.090, 0.250, 0.360, 2.0, 3.0, 4.0]) # Independent variable (X) price_dollars = np.array([18.95, 25.00, 38.95, 61.79, 197.00, 304.79, 397.49]) # Dependent variable (Y)

Add a constant term for intercept in the regression model

X = sm.add_constant(capacity_TB)

Perform linear regression

model = sm.OLS(price_dollars, X).fit()

Get R-squared value

r_squared = model.rsquared r_squaredThe $R^2$ value is 0.9982 (rounded to four decimal places) or 99.82% when rounded to two decimal places.

Interpretation:

This means that 99.82% of the variation in price can be explained by the capacity of the disk drives, indicating a very strong linear relationship between capacity (in TB) and price (in $).

Would you like a deeper breakdown of the regression model?

Related Questions:

1. How is $R^2$ calculated in a regression model?
2. What does a high $R^2$ value indicate about the model?
3. How can we check if a linear model is the best fit for the data?
4. What other regression models can be used for this dataset?
5. How do we interpret the slope and intercept in this regression equation?

Tip:

If $R^2$ is close to 1, it means the model fits the data well. However, it's important to check residuals to ensure there is no pattern indicating a non-linear relationship.