Make a scatterplot of the data and graph the function f(x)= -8x^{2} + 95x + 745. Make a residual plot and describe how well the function fits the data. begin{array}{|c|c|} hline text{Price Increase} & 0 & 1 & 2 & 3 & 4 hline text{Sales} & 730 & 850 & 930 & 951 & 1010 hline end{array}

Question
Scatterplots
asked 2021-01-08
Make a scatterplot of the data and graph the function \(\displaystyle{f{{\left({x}\right)}}}=\ -{8}{x}^{{{2}}}\ +\ {95}{x}\ +\ {745}.\) Make a residual plot and describe how well the function fits the data. \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Price Increase}&{0}&{1}&{2}&{3}&{4}\backslash{h}{l}\in{e}\text{Sales}&{730}&{850}&{930}&{951}&{1010}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)

Answers (1)

2021-01-09
Step 1 By drawing the curve \(\displaystyle{f{{\left({x}\right)}}}=\ -{8}{x}^{{{2}}}\ +\ {95}{x}\ +\ {745}\) (expected) and marking the points in the graph (actual) we get it is given below. The residual value is calculated as \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Residual value}=\text{Actual value}-\text{Expected value}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
\(\displaystyle\text{Residual value at}\ {x}={0},\ {R}_{{{0}}}={730}\ -\ {745}\)
\(\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}-{15}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
\(\displaystyle\text{Residual value at}\ {x}={1},\ {R}_{{{1}}}={850}\ -\ {832}\)
\(\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{18}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
\(\displaystyle\text{Residual value at}\ {x}={2},\ {R}_{{{2}}}={930}\ -\ {903}\)
\(\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{27}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
\(\displaystyle\text{Residual value at}\ {x}={3},\ {R}_{{{3}}}={951}\ -\ {958}\)
\(\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}-{7}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\)
\(\displaystyle\text{Residual value at}\ {x}={4},\ {R}_{{{4}}}={1010}\ -\ {997}\)
\(\displaystyle={b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}+{13}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}\) image Step 2 By plotting the residual value to the graph which is given below, we can see that the points are randomly scattered through the graph. This indicates that the line is a Good Fot. image
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