Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TBequals1000 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) 0.080 0.130 0.280 0.490 2.0 3.0 4.0

Price (in $) 28.00 41.45 50.00 74.99 215.79 366.99 393.00

What is the value of Upper R squared?

What is the interpretation of Upper R squared? The value of Upper R squared equals _____ indicates the percentage of the variability in the price of these disk drives that can be explained by the variability in the capacity of the drives. (Round to two decimal places as needed.)

Since the correlation coefficient and subsequently R squared are both very close to 1, this indicates a very high positive correlation, close to a perfect positive correlation between price and capacities of external storage drives.

Explanation:

Let the capacity be x

And the price be y

Capacity (in TB) 0.080 0.130 0.280 0.490 2.0 3.0 4.0

Price (in $) 28.00 41.45 50.00 74.99 215.79 366.99 393.00

Mean of capacity, xbar = (Σx/n)

Note that Σx represents the sum of all the capacities given = 10.01

N = Sample size = 7

mean of capacity, xbar = 1.43 (in TB)

Mean of price, ybar = (Σy/n)

Note that Σy represents the sum of all the prices given = 1170.26

N = Sample size = 7

Mean of price, ybar = $167.18

- The formula for the correlation coefficient is given in the first attached image.

- xbar and ybar are given as x and y with bars over their heads.

- xᵢ and yᵢ represent each of the variables of capacities and price respectively.

- And n ranges from 1 to 7.

- The graph of price against capacities is also attached in the second attached image

On computing the correlation coefficient,

The correlation coefficient = 0.99033

R squared = 0.99033² = 0.981

The correlation coefficient and R squared are very close to 1.

Hope this Helps!!!

MrRoyal MrRoyal · Answer 2 · 2022-04-16T18:54:58+02:00

The value of R^2 is 98.07% and it indicates that 98.07% of the variability in the price of the disk drives that can be explained by the variability in the capacity of the drives

How to determine the coefficient of determination, R^2?

The dataset is given as:

Capacity (in TB) 0.080 0.130 0.280 0.490 2.0 3.0 4.0

Price (in $) 28.00 41.45 50.00 74.99 215.79 366.99

To calculate the R^2 of the dataset, we make use of a graphing calculator with the following calculation summary:

X Values

∑ = 9.98

Mean = 1.426

∑(X - Mx)2 = SSx = 15.113

Y Values

∑ = 1170.22

Mean = 167.174

∑(Y - My)2 = SSy = 150690.894

X and Y Combined

N = 7

∑(X - Mx)(Y - My) = 1494.524

The correlation coefficient, R is calculated using:

R = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

This gives

R = 1494.524 / √((15.113)(150690.894))

R = 0.9903

Square both sides to determine the coefficient of determination, R^2

R^2 = 0.9807

Express as percentage

R^2 = 98.07%

Hence, the value of R^2 is 98.07%

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