Situation: The Ipod Touch has been out for two years now and a lot of data has been collected.

Question

Relevant Relationship:

There is a functional relationship between Price of an IPod Touch, "p" and Weekly Demand, "s".

Below is a table of data that have been collected

Price,"p",($) Weekly Demand,"s" ,(1,000s)

150 208

170 208

190 194

210 189

230 182

250 175

A.. Find the linear model that best fits this data using regression and enter the model below

(for entry round the linear parameter value to nearest 0.01 and constant parameter to nearest 1)

s=T(p) =

B. The squared correlation coefficient r^2 was ____ (above/below) 0.95

=

(note: values less than 0.95 MAY mean the model is not appropriate for making predictions)

Now answer these two questions using the UNROUNDED model parameters

C. What does the model predict will be the weekly demand if the price of an ipod touch is $201? (nearest 100)

=

D. According to the model at what should the price be set in order to have a weekly demand of 176,700 ipod Touches? (nearest $1) = $

Answer 1

Hi Anchal,

To get the regression line/best fit linear model, do the following within TI-83 Plus:

1. Go to STAT--EDIT--Create two lists: one for price, one for weekly demand. Enter all values.
2. Go to STAT--CALC--LinReg (ax + b) L_1, L₂ Note calculator defines a as slope, rather than m. Same meaning.
3. You get: a=m= -0.354...b=263.52...
4. Round these per instructions and sub into y=mx + b equation; this is essentially your model:

A. y=-0.35x + 264

1. r² is also displayed on your screen. It's 0.964..., so

B.:r² >0.95.

C. Plug the price you are given into the equation above but do not round:

y^= -0.35428....(201) + 263.52....

y^=192.31 or, rounded to nearest 100,

y^=200

D. This is basically the same process in reverse. Remember we were given data in 1000s for demand, so we have to divide 176700 by 1000 to get 176.7. Sub this into initial equation, again unrounded, for y:

176.7= -0.35428....x + 263.52....

Subtract 263.52.... on both sides

-86.823....= -0.35428....x

Divide both sides by -0.35428....

x=245.07, or rounded to nearest whole dollar

x=$245

Formula for computing slope is more complex than the one I posted in earlier problem. Another tutor pointed that out to me. Correct formula is extremely complex and it's probably best to use the calculator method to find slope and regression line. I hope this helps and sorry for earlier mistake.