5 Mark Each

Question 15 Marks

A sample of seven students is taken from the students, who came to study from abroad in the current year in a university of Gujarat State. The information of their intelligence quotient $(I.Q)\ X$ and the marks obtained by them in a test of $75$ marks $Y$ is as follows.
$\Sigma x=675, \Sigma y=361$ $\Sigma\left(\frac{x-95}{5}\right)^2=76, \Sigma(y-50)^2=641$
$\Sigma\left(\frac{x-95}{5}\right)^2(y-50)=213$
Obtain the regression line of $Y$ on $X$ from this data and check the reliability of the regression model.

Answer

$\hat{y}=-2.43+0.56 x, R^2=0.94$ Regression model is reliable.

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Question 25 Marks

Obtain the regression line of production of groundnuts on the consumption of fertilizers from this data. Estimate the production of groundnuts if the consumption of fertilizers is $250 \ kg$.

Production of groundnuts $y (10,000\ kg)$	$20$	$24$	$16$	$18$	$28$	$32$	$17$
Consumption of fertilizers $x (10\ kg)$	$10$	$16$	$10$	$12$	$17$	$18$	$14$

Answer

$\hat{y}=0.34+0.29 x$, For $x=100($ lakh $₹), \hat{y}=29.34 ($crore $₹), e=10.66$

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Question 35 Marks

A sample data collected to study the effects of the consumption of fertilizer $(X)$ on the production of groundnuts $(Y)$ are as follows:

Production of groundnuts $y (10,000\ kg)$	$20$	$24$	$16$	$18$	$28$	$32$	$17$
Consumption of fertilizers $x (10\ kg)$	$10$	$16$	$10$	$12$	$17$	$18$	$14$

Obtain the regression line of production of groundnuts on the consumption of fertilizers from this data. Estimate the production of groundnuts if the consumption of fertilizers is $250\ kg$.

Answer

$\hat{y}=0.38+1.57 x$, When the consumption of fertilizer is $250 \ kg$, the yield in the farm will be $3,96,300 \ kg$.

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Question 45 Marks

The following results are obtained for a particular data : $n=6, \Sigma x=40, \Sigma y=58, \Sigma x y=431$ and $\Sigma x^2=316$ Later on, it was found that one pair was taken as $(15,12)$ instead of $(12,15)$. Obtain the regression line of $Y$ on $X$ from this data and estimate $Y$ for $X=7$.

Answer

$\hat{y}=-39.31+8.02 x$, For $x=7, \hat{y}=16.83$

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Question 55 Marks

Obtain the regression line of sale of raincoats on the rain from the data given below about the rains $X$ (in $cms$ ) and the sale of raincoats $Y ($in $100$ pieces$)$ of various districts during the monsoon season. Also find coefficient of determination and interpret it.

District	$A$	$B$	$C$	$D$	$E$	$F$	$G$
Rain $x(cms)$	$65$	$52$	$38$	$30$	$100$	$70$	$50$
Sales of raincoats $y (100$ pieces$)$	$1.7$	$1.8$	$1$	$1$	$2.32$	$1.9$	$2$

Answer

$\hat{y}=0.51+0.02 x, R^2=0.72$ The assumption of linear regression is valid

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Question 65 Marks

The following results are obtained showing the relation between the price of mobile phones $X( $in thousand $₹)$ and their demand $Y ($in pieces$)$ on a particular day.

Price of mobile phone $x ($thousand $₹)$	$8.5$	$6$	$20$	$12.5$	$14$	$18.5$	$24.5$
Demand $y ($pieces$)$	$40$	$30$	$120$	$80$	$45$	$100$	$15$

Obtain the regression line of $Y$ on $X$ from this data and if the price of the mobile is $₹ 15,000$ then obtain its estimated demand.

Answer

$\hat{y}=39.59+1.47 x$, For $x=15 ($thousand $₹), \hat{y}=62$ items

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Question 75 Marks

The data of the sales $($in lakh $₹)$ of two commodities made by a manufacturing company in the last six months are as follows :

Sales of commodity $Ax ($ lakh $₹)$	$7$	$5$	$2$	$10$	$8$	$4$
Sales of commodity $By ($in lakh $₹)$	$10$	$8$	$6$	$8$	$5$	$5$

Obtain the regression line of $Y$ on $X$ and find the value of error when the sales of commodity $A$ is $₹ 2,00,000$.

Answer

$\hat{y}=5.56+0.24 x$, For $x=2,00,000(₹), \hat{y}=6,04,000(₹), e=-0.04$

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Statistics 5 Mark Each

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