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 are shown below: Number of Pages (2) Cost(y) 839 103.29 644 86.84 272 34.92 905 104.55 339 54.29 927 112.97 691 89.01 805 99.55 500 59 711 96.21 810 98.1 A student calculates a linear model y (Please show your answers to two decimal places) Use the model to estimate the cost when number of pages is 979. Cost - $ (Please show your answer to 2 decimal places.) Check Answer

Answer 1

Solution :

W have to find the linear regression equation.

Where ;

$b_1$ = Slop of regression equation

$b_0$ = Intercept

$b_1 = \frac{\sum{(x - \bar{x})(y - \bar{y})}}{\sum{(x-\bar{x})^2}}$

$b_0 = \bar{y}-b_1\bar{x}$

By using Excel Calculation :

	Number of pages (X)	Cost (Y)	(X - Mean(X)	(X -Mean(X))^2	(Y - Mean(Y))	(X - Mean(X))(Y - Mean(Y))
	839	103.29	162.363636	26361.95041	17.9509091	2914.574876
	644	86.84	-32.636364	1065.132231	1.50090909	-48.98421488
	272	34.92	-404.63636	163730.5868	-50.4190909	20401.3976
	905	104.55	228.363636	52149.95041	19.2109091	4387.073058
	339	54.29	-337.63636	113998.314	-31.0490909	10483.30215
	927	112.97	250.363636	62681.95041	27.6309091	6917.774876
	691	89.01	14.3636364	206.3140496	3.67090909	52.72760331
	805	99.55	128.363636	16477.22314	14.2109091	1824.163967
	500	59	-176.63636	31200.40496	-26.3390909	4652.44124
	711	96.21	34.3636364	1180.859504	10.8709091	373.5639669
	810	98.1	133.363636	17785.8595	12.7609091	1701.84124
Sum	7443	938.73		486838.5455		53659.87636
Mean	676.6363636	85.33909
			b1	0.110221093
			b0	10.75949167

1) Regression equation is ;

2) If the Number of pages (X) = 979 then Estimated cost is;

$\hat{y} = 0.11*979+10.76$

$\hat{y} = 118.45$

Cost = $ 118.45

Excel Output of Regression :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.980396817
R Square	0.961177918
Adjusted R Square	0.956864354
Standard Error	5.151971503
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	5914.450198	5914.45	222.8268	1.17666E-07
Residual	9	238.8852933	26.54281
Total	10	6153.335491
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	10.75949167	5.232073589	2.056449	0.069881	-1.076281055	22.59526	-1.07628	22.59526
Number of pages (X)	0.110221093	0.007383818	14.92739	1.18E-07	0.093517736	0.126924	0.093518	0.126924