Question

statistics students in oxnard college sampled 11 textbooks in the condor bookstore and recorded the number of pages in each textbook and its cost. the bivariate data is shown below,

number of pages ($x$)	cost($y$)
983	71.15
891	69.55
356	44.8
384	41.2
719	55.95
855	61.75
230	38.5
762	50.1
218	23.9
335	31.75

a student calculates a linear model
$y=square x+square$. (please show your answers to 2 decimal places)

use the rounded equation above to estimate the cost when number of pages is 503
cost = $ square$ (please show your answer to 2 decimal places.)

Explanation:

Step1: Calculate sums

Let \(n = 11\). Calculate \(\sum x\), \(\sum y\), \(\sum x^2\), \(\sum xy\).
\(\sum x=487 + 983+891+356+384+719+855+230+762+218+335 = 6020\)
\(\sum y=37.35 + 71.15+69.55+44.8+41.2+55.95+61.75+38.5+50.1+23.9+31.75 = 526.05\)
\(\sum x^2=487^2+983^2+891^2+356^2+384^2+719^2+855^2+230^2+762^2+218^2+335^2=487^2 + 966289+793881+126736+147456+516961+731025+52900+580644+47524+112225 = 4257942\)
\(\sum xy=487\times37.35+983\times71.15+891\times69.55+356\times44.8+384\times41.2+719\times55.95+855\times61.75+230\times38.5+762\times50.1+218\times23.9+335\times31.75=18289.45+70030.45+61969.05+15948.8+15820.8+40228.05+52796.25+8855+38176.2+5210.2+10646.25 = 337970.5\)

Step2: Calculate slope \(m\)

The formula for the slope \(m\) of the regression - line \(y = mx + b\) is \(m=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}\).

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Step3: Calculate intercept \(b\)

The formula for the intercept \(b\) is \(b=\frac{\sum y - m\sum x}{n}\).

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Step4: Estimate cost

The linear model is \(y = 0.05x+20.46\). When \(x = 503\), \(y=0.05\times503+20.46=25.15+20.46 = 45.61\)

Answer:

The linear - model is \(y = 0.05x+20.46\). The estimated cost when \(x = 503\) is \(\$45.61\)