Questions: 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. For this data, we want to predict Price from Capacity. Complete parts a through i below. Click the icon to view the disk drive data and summary statistics. b1=142.35 (Round to two decimal places as needed.) b) What does the slope mean, in this context? A. It indicates the additional price in dollars for each additional TB of capacity. B. It is meaningless and should not be interpreted. C. It indicates the price for a hard drive with no capacity. This could be interpreted as the cost of the parts common to all drives. D. It indicates the additional capacity in TB for each additional dollar of price. E. It indicates the additional capacity in gigabytes for each additional dollar of price. c) Find the intercept, b0. b0= (Round to two decimal places as needed.)

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. For this data, we want to predict Price from Capacity. Complete parts a through i below. Click the icon to view the disk drive data and summary statistics. b1=142.35 (Round to two decimal places as needed.) b) What does the slope mean, in this context? A. It indicates the additional price in dollars for each additional TB of capacity. B. It is meaningless and should not be interpreted. C. It indicates the price for a hard drive with no capacity. This could be interpreted as the cost of the parts common to all drives. D. It indicates the additional capacity in TB for each additional dollar of price. E. It indicates the additional capacity in gigabytes for each additional dollar of price. c) Find the intercept, b0. b0= (Round to two decimal places as needed.)
Transcript text: Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where $1 \mathrm{~TB}=1000$ gigabytes, or about a trillion bytes. A survey of prices for external disk drives found the data shown to the right. For this data, we want to predict Price from Capacity. Complete parts a through i below. Click the icon to view the disk drive data and summary statistics. $b_{1}=142.35$ (Round to two decimal places as needed.) b) What does the slope mean, in this context? A. It indicates the additional price in dollars for each additional TB of capacity. B. It is meaningless and should not be interpreted. C. It indicates the price for a hard drive with no capacity. This could be interpreted as the cost of the parts common to all drives. D. It indicates the additional capacity in TB for each additional dollar of price. E. It indicates the additional capacity in gigabytes for each additional dollar of price. c) Find the intercept, $b_{0}$. $\mathrm{b}_{0}=$ $\square$ (Round to two decimal places as needed.)
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Solution

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Solution Steps

To solve the given questions, we need to understand the context of linear regression where the price of disk drives is predicted based on their capacity.

a) The slope \( b_1 \) represents the change in price for each additional terabyte of capacity. In this context, the correct interpretation is that it indicates the additional price in dollars for each additional TB of capacity.

b) To find the intercept \( b_0 \), we need to use the formula for the intercept in a linear regression model, which is typically calculated using the means of the dependent and independent variables along with the slope.

Solution Approach
  • a) The slope \( b_1 = 142.35 \) indicates the additional price in dollars for each additional TB of capacity.
  • b) The intercept \( b_0 \) can be calculated using the formula: \( b_0 = \bar{y} - b_1 \times \bar{x} \), where \( \bar{y} \) is the mean price and \( \bar{x} \) is the mean capacity.
Step 1: Interpret the Slope

The slope \( b_1 = 142.35 \) represents the change in price for each additional terabyte of capacity. In this context, it indicates the additional price in dollars for each additional TB of capacity. Therefore, the correct interpretation is:

The answer is A.

Step 2: Calculate the Intercept

To find the intercept \( b_0 \), we use the formula for the intercept in a linear regression model:

\[ b_0 = \bar{y} - b_1 \times \bar{x} \]

Given:

  • \( b_1 = 142.35 \)
  • \( \bar{x} = 5 \) (mean capacity in TB)
  • \( \bar{y} = 800 \) (mean price in dollars)

Substitute these values into the formula:

\[ b_0 = 800 - 142.35 \times 5 = 88.25 \]

Final Answer

\(\boxed{b_0 = 88.25}\)

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