Question

statistics students in oxnard college sampled 9 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)
782	69.56
779	77.32
328	43.24
586	59.88
768	68.44
638	68.04
505	65.4
419	40.52

a student calculates a linear model y = x +. (please show your answers to 2 decimal places)
use the rounded equation above to estimate the cost when number of pages is 210. cost = $ (please show your answer to 2 decimal places.)

Explanation:

Step1: Calculate sums

Let $n = 9$.
Calculate $\sum x$, $\sum y$, $\sum x^2$, $\sum xy$.
$\sum x=790 + 782+779+328+586+768+638+505+419 = 5695$
$\sum y=86.2 + 69.56+77.32+43.24+59.88+68.44+68.04+65.4+40.52 = 578.5$
$\sum x^2=790^2+782^2+779^2+328^2+586^2+768^2+638^2+505^2+419^2$
$=624100+611524+606841+107584+343396+589824+407044+255025+175561 = 3720899$
$\sum xy=790\times86.2+782\times69.56+779\times77.32+328\times43.24+586\times59.88+768\times68.44+638\times68.04+505\times65.4+419\times40.52$
$=68098+54395.92+60232.28+14182.72+35089.68+52561.92+43309.52+33027+17077.88 = 378984.92$

Step2: Calculate slope $m$

The formula for the slope $m$ of the regression - line is $m=\frac{n\sum xy-\sum x\sum y}{n\sum x^2 - (\sum x)^2}$
$n\sum xy=9\times378984.92 = 3410864.28$
$\sum x\sum y=5695\times578.5 = 3293557.5$
$n\sum x^2=9\times3720899 = 33488091$
$(\sum x)^2=5695^2 = 32433025$
$m=\frac{3410864.28 - 3293557.5}{33488091-32433025}=\frac{117306.78}{1055066}\approx0.11$

Step3: Calculate intercept $b$

The formula for the intercept $b$ is $b=\bar{y}-m\bar{x}$, where $\bar{x}=\frac{\sum x}{n}=\frac{5695}{9}\approx632.78$ and $\bar{y}=\frac{\sum y}{n}=\frac{578.5}{9}\approx64.28$
$b = 64.28-0.11\times632.78=64.28 - 69.6058\approx - 5.33$

The linear model is $y = 0.11x-5.33$

Step4: Estimate cost when $x = 210$

Substitute $x = 210$ into the equation $y=0.11x - 5.33$
$y=0.11\times210-5.33=23.1-5.33 = 17.77$

Answer:

$y = 0.11x-5.33$; $17.77$