Download App

LINEAR REGRASSION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsLINEAR REGRASSION3 Marks
Question
The following measures are obtained to study the relation between rainfall in cm $( X )$ and yield of Bajri in quintal per hectare $( Y )$ in ten different regions during monsoon $n=10, \bar{x}=40, \bar{y}=175, S _{x}=12, \operatorname{Cov}(x, y)=360$. Obtain the regression line of yield $Y$ on rainfall $X$.
✓

Answer

$b = \frac{Cov(x,y)}{S_{x}^{2}} = \frac{360}{144} = 2.5$.
$a = \overline{y} - b\overline{x} = 175 - 2.5(40) = 175 - 100 = 75$.
Regression line : $\hat{y} = 75 + 2.5x$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Each" from LINEAR REGRASSION→LINEAR REGRASSION — all question types→Statistics STD 12 Commerce question papers→Gujarat Board STD 12 Commerce question papers→Gujarat Board question paper generator→

Similar questions

The following measures are obtained to study the relation between rainfall in $cm .( X )$ and yield of Bajri in quintal per hectare $( Y )$ in ten different regions during monsoon :$n =10, \overline{ x }=40, \overline{ y }=175, S _{ x }=12, \operatorname{Cov}( x , y )=360$Obtain the regression. line of yield, $Y$ on rainfall $X$. Estimate the yield of Bajri when the rainfall $X$ is $30 cm$. E
→
A factory produces screws of different lengths. The length $($in $cm)$ of screw is denoted by $x$. The events $A_{1}$ and $A_{2}$ are defined as follows in the experiment of finding the length of selected screws. Find the events showing union event $A_{1} \cup A_{2}$ and intersection event $A_{1} \cap A_{2}$.
→
The index numbers of food and clothing among the different groups of cost of living are $150$ and $224.7$ respectively for the year $2015.$ The price of fuel has increased by $220 \%$. The expense on rent has increased from $₹ 4000$ to $₹ 6000$ and miscellaneous expenses increased by $1.75$ times. If the expenditure for the first four groups are $40 \%, 18 \%, 12 \%$ and $20 \%$ respectively, find the cost of living index number for the year $2015$ and interpret it.
→
Find $\frac{d y}{d x}$ for $y=x^{3}+\sqrt{x}-\frac{4}{x}+\frac{1}{\sqrt[3]{x}}+\frac{1}{4}$.
→
Two variables $X$ and $Y$ are mutually dependent variables, $\Sigma(x-\bar{x})(y-\bar{y})=$ $-200, n S_{x}^{2}=125 ; n S_{y}^{2}=500$, find $b_{y n}$
→
The mean of a normal distribution is $150$ and Its variance is $625 .$ If $(1)\ P\left[X \leq k_{1}\right]=$ $0.7257$, $(2)\ P\left[k_{2} \leq X \leq 140\right]=0.3218$ and $(3)\ P\left[X \geq k_{3}\right]=0.1038$, find the values of $k_{1}, k_{2}$ and $k_{3}$.
→
The demand function of a commodity is $p=12-\sqrt{x}$. Find the elasticity of demand when the price is $9$ units and interpret it.
→
Give difference between fixed base and chain base methods.
→
The distribution of a random variable X is $p (x)=K•^5P_x, x=0, 1, 2, 3, 4, 5$. Find constant K and mean of this distribution.
→
A random variable X denotes the number of accidents per year in a factory and the probability distribution of X is given below :
X = x01234
p(x)4K15K25K5KK
(i) Find the constant K.
(ii) Find the probability of the event that one or two accidents will occur in this factory during the year.
→