Answer :
Answer:
[tex]\textsf{A)}\quad s=T(p)=\boxed{-0.38p+268}[/tex]
B) 184,400 or 185,500
C) $61 or $62
Note that the first answer for parts B and C has been calculated using the rounded model parameters, whereas the second answer in both parts has been calculated using the unrounded model parameters.
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Step-by-step explanation:
The given table of data shows the functional relationship between the price (p) of an IPod Touch and the weekly demand (s):
[tex]\begin{array}{|c|c|}\cline{1-2} \textsf{Price, $p$, (\$)} & \textsf{Weekly Demand, $s$, (1,000s)} \\\cline{1-2} 150 & 210 \\\cline{1-2} 170 & 203 \\\cline{1-2} 190 & 200 \\\cline{1-2} 210 & 191 \\\cline{1-2} 230 & 183 \\\cline{1-2} 250 & 171 \\\cline{1-2} \end{array}[/tex]
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Part A
To find the linear model that best fits this data using regression, enter the data into a linear regression calculator, where the price (p) is the independent variable, and the weekly demand (s) is the dependent variable.
After entering the data from the given table into a statistical calculator we get:
[tex]a = -0.37714285...=-0.38[/tex]
[tex]b = 268.428571...=268[/tex]
where a is the slope (rounded to the nearest hundredth) and b is the y-intercept (rounded to the nearest 1) of a linear equation.
Therefore, the linear regression model is:
[tex]s=T(p)=\boxed{-0.38p+268}[/tex]
[tex]\dotfill[/tex]
Part B
To find the weekly demand if the price of an ipod touch is $220, substitute p = 220 into the regression model and solve for s.
Using the ROUNDED parameters:
[tex]s=T(220)=-0.38(220)+268\\\\s=T(220)=-83.6+268\\\\s=T(220)=184.4[/tex]
Using the UNROUNDED parameters:
[tex]s=T(220) = -0.37714285...(220) + 268.428571...\\\\s=T(220) =185.457142857142...\\\\s=T(220)=185.457[/tex]
Therefore, if the price of an ipod touch is $220, the weekly demand will be:
- ROUNDED parameters = 184,400
- UNROUNDED parameters = 185,500
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Part C
To determine the price at which the ipod should be set to have a weekly demand of 245,000, substitute s = 245 into the regression model and solve for p:
Using the ROUNDED parameters:
[tex]-0.38p+268=245\\\\\\-0.38p=-23\\\\\\p=\dfrac{-23}{-0.38}\\\\\\p=60.526315789...\\\\\\p=61[/tex]
Using the UNROUNDED parameters:
[tex]-0.37714285...(p) + 268.428571...=245\\\\p=62.12121212...\\\\p=62[/tex]
Therefore, to achieve a weekly demand of 245,000, the ipod should be set at a price of:
- ROUNDED parameters = $61
- UNROUNDED parameters = $62
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Additional Information
You have not specified if you are to use the ROUNDED or the UNROUNDED model parameters to answer parts B and C, so I have provided both.