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 in chart. For this data, we want to predict Price from Capacity. A). Find the slope estimate b1. _________B). Find the intercept b0. ___________C). Write equation that predicts Price from Capacity - price= ______ + (_____) capacityD). What would you predict price of a 20.0 TB disk? _______

Answer 1

To compute the slope, intercept, and equation to predict the Price, we will use the formulae below:

For the equation

`\bar{y}=b(\bar{x})+a`

For the slope

`b=r((S_y)/(S_x))`

For the intercept

`a=\bar{y}-b\bar{x}`

In this case, we have the following data given:

`\begin{gathered} \bar{x}=7.611,S_x=9.85,r=0.987 \\ \bar{y}=784.173,S_y=1419.89 \end{gathered}`

Part A

Upon substituting the above into the formula, we will have

`b=0.987((1419.89)/(9.85))=141.41`

Hence slope = 141.41

Part B

`\begin{gathered} a=\bar{y}-\bar{bx} \\ a=784.173-141.41(7.611) \\ a=-292.099 \end{gathered}`

Hence, Intercept =-292.099

PART C

The equation that can be used to predict Price from Capacity

`\begin{gathered} \text{Price}=\text{intercept}+(\text{slope)capacity} \\ \text{Price}=-292.099+(141.41)\text{capacity} \end{gathered}`

Therefore, the equation is

Price=-292.099+(141.41)capacity

Part D

To predict the price of a 20.0TB disk, we will simply set the capacity= to 20 and then simplify

`\begin{gathered} P_(20TB)=-292.099+141.41(20) \\ P_(20TB)=2536.10 \end{gathered}`

Hence, the predicted price is=2536.10