Download App

LINEAR REGRASSION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsLINEAR REGRASSION3 Marks
Question
Explain : Co-efficient of determination.
✓

Answer

It is the square of the correlation co-efficient between the observed value of dependent variable $Y$ and its estimated values.
  • The measure of the closeness of the correlation between variable $Y$ and $X$ is given by co-efficient of determination.
  • It is denoted by $R^2.$
  • The least value of $R^2 = 0$ and maximum value is $1.$
  • Regression line can be obtained for one variable with a given value of another variable but validity of that value depends on correlation of this two variables.
  • If their is perfect correlation $(r=1)$ between two variables, then we can say that assumption of linear regression is proper but correlation between two variables, then we can say that assumption of linear regression is Proper but correlation between two variables is nearer to $‘0’,$ then we can say that assumptions are not proper.
  • So, trustworthiness of regression line depends on value of correlation.
  • So, this value is known as co-efficient of determination, which is denoted by $R^2.$
  • Maximum value of $R$ is $1.$
  • Minimum value of $R^2$ is $0,$ which denotes lack or correlation between two variables.
  • If co-efficient of determination $R^2 = 1$ or nearer to $1,$ then it can be said that assumption of linear correlation between $Y$ and $X$ is valid.
  • If the co-efficient of determination $R^2= 0$ or nearer to $0,$ it can be said that assumption of linear correlation between $Y\ \&\ X$ is not valid.
  • But it can not be said that there is no relation between $Y$ and $X.$
  • Co-efficient of determination is a square of correlation coefficient. 80, one can say that $R^2 = r^2$
  • So, value of $R^2$ is $0 \leq R^2 \leq 1.$
  • Here, $R^2 = ($Co-efficient Correlation $ Y,)^2 = \{r(Y,X)\}^2$
$= \{r(Y,)\}^2 = r^2$
$= \{r(Y,a+bx)\}^2 \therefore R^2 = r^2$
  • Uses :
  • $(1)$ To know the trustworthiness of assumptions, estimates obtained by using the line of regression.
  • $(2)$ To check the validity of the assumption of linear correlation between variable $Y\ \&\ X.$

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

If $u =8( x -30), v =5( y -20)$ and $b_{y z}=2.4$. find the value of $b_{m}$
→
Obtain derivative of $f(x)=x^{3}$ with the help of definition.
→
Express the following neighbourhood form in modulus form: $(1)\ N(-1,0.01)\ (2)\ N(-0.2,0.4)\ (3)\ N(5,2)$
→
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 following data is available for the variable $y$ of a time series. Fit a linear equation from it.
$n=9, \Sigma y=214, \Sigma t y=1051$
→
The information about six different items used in the production of an electronic item is as follows. Find the Index Number and Interpret it :
ItemsABCDEF
Weight51010302025
Percentage Price Relative290315280300315320
→
As compared to the year $2015,$ the prices of three items $A, B$ and $C$ have increased by $90\%, 120\%$ and $75\%$ respectively in the year $2017,$ while the prices of remaining two items $D$ and $E$ have decreased by $10\%$ and $15\%$ respectively. Relative importance of $A$ is twice that of $B$ and relative importance of $C$ is thrice that of $A.$ Relative importance of $D$ and $E$ are one and half times that of $C.$ Construct general index number of price for $2017.$
→
There are $10$ ice cream cones in a box of which $3$ cones weight less than the specification and the rest of the $7$ cones have the specified weight. Two cones are randomly selected one by one with replacement. Find the probability that both the cones selected weigh less than the specified weight.
→
$\lim _{x \rightarrow 0} \frac{\sqrt{1+x}-\sqrt{1-}}{x}$
→
State the properties of standard normal distribution.
→