Predicting price from capacity
2.
Disk drives have been getting
larger. Their capacity in 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 following data:
Capacity (in TB) Price (in $)
.080 29.95
.120 35.00
.200 299.00
.250 49.95
.320 69.95
1.0 99.00
2.0 205.00
4.0 449.00
4.
A company that relies on
internet-based advertising linked to key search terms wants to understand the
relationship between the amount it spends on this advertising and revenue (in
$).
a) Which
variable is the explanatory or predictor variable?
b) Which
variable is the response variable?
c) Which
variables would you plot on the x axis?
14.
For the disk drives in problem 2
above, we want to predict Price from Capacity.
a) Find
the slope estimate, b1.
b) What
does it mean in this context?
c) Find
the intercept, b0.
d) What
does it mean in this context? Is it meaningful?
e) Write
down the equation that predicts Price from Capacity.
f) What
would you predict for the price of a 3.0 TB disk?
g) You
have found a 3.0 TB drive for $300. Is this a good buy? How much would you save
compared to what you expected to pay?
h) Does
the model overestimate or underestimate the price?
54.
An online clothing retailer
examined their transactional database to see if total yearly Purchases ($) were
related to customers’ Income ($). (You may assume that the assumptions and
conditions for regression are met). The least squares linear regression is:
Purchase = -31.6 + 0.012 Income.
a) Interpret
the intercept in the linear model.
b) Interpret
the slope in the linear model.
c) If
a customer has an Income of $20,000, what is his predicted total yearly
Purchases?
d) This
customer’s yearly Purchases were actually $100. What is the residual using this
linear model? Did the model provide an underestimate or overestimate for this
customer?
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