Make a scatterplot of the data and graph the function f(x)= -8x^{2} + 95x + 745.

Question

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

Answer 1

Step 1 By drawing the curve $f (x) = - 8 x^{2} + 95 x + 745$ (expected) and marking the points in the graph (actual) we get it is given below. The residual value is calculated as $\begin{array}{cc} Residual value = Actual value - Expected value \end{array}$
$Residual value at x = 0, R_{0} = 730 - 745$
$= \begin{array}{cc} - 15 \end{array}$
$Residual value at x = 1, R_{1} = 850 - 832$
$= \begin{array}{cc} + 18 \end{array}$
$Residual value at x = 2, R_{2} = 930 - 903$
$= \begin{array}{cc} + 27 \end{array}$
$Residual value at x = 3, R_{3} = 951 - 958$
$= \begin{array}{cc} - 7 \end{array}$
$Residual value at x = 4, R_{4} = 1010 - 997$
$= \begin{array}{cc} + 13 \end{array}$

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.

Make a scatterplot of the data and graph the function f(x)= -8x^{2} + 95x + 745.

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