Sample QuestionsPART 1 : LINEAR REGRASSION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $r=0.6$, how much percent of the total variations in the dependent variable can not be explained by the regression model ?
Answer: C.
View full solution →What will be the value of correlation coefficient if the coefficient of determination between two variables is $0.49$ ?
- A
$-0.49$
- B
$+0.49$
- ✓
$\pm 0.7$
- D
$+0.51$
Answer: C.
View full solution →What will be the value of $b_{y x}$ if $v=15(y-75), u=6(x-50)$ and $b_{v u}=3.5$ ?
- ✓
$1.4$
- B
$0.03$
- C
$8.75$
- D
$315$
Answer: A.
View full solution →If $u=\left(\frac{x-400}{100}\right), v=\left(\frac{y-25}{5}\right)$ and $b_{y x}=2.8$ then what will be the value of $b_{v u} ?$
Answer: D.
View full solution →If $R^2=r^2=1$ then what type of correlation is obtained between the variables $X$ and $Y$ ?
- A
partial positive linear correlation
- B
partial negative linear correlation
- ✓
perfect linear correlation
- D
lack of linear correlation
Answer: C.
View full solution →Write the value of error for the points which are on the regression line obtained by the method of least square?
How will be the error if the points are above the regression line obtained by the method of least square ?
If regression line $\hat{y}=95-6.5 x$ shows the relation between $X$ and $Y$, state the sign of correlation coefficient.
View full solution →Find $\hat{y}$ for $X=60$ if regression line is $\hat{y}=45.32+2.85 x$.
View full solution →If $r=0.75, S_x=6$ and $S_y=14$ then what will be the value of $b_{y x}$ ?
View full solution →The following results are obtained while studying the experience $($in year$)$ of ten salesmen and the sales $($lakh $₹)$ achieved by them.
| Particular |
Experience of salesmen $($year$)$ |
Sales $($lakh $₹)$ |
| Mean |
$3.5$ |
$40.6$ |
| Standard deviation |
$2.1$ |
$6.5$ |
| Sum of the products of the deviations taken from the mean |
$100$ |
|
Obtain regression line of $Y$ on $X$ from this data. View full solution →The following results are obtained while studying the relation between the marks of Statistics and Elements of Accounts for $60$ students of standard $12.$ Obtain regession line of the marks of Elements of Accounts on the marks of Statistics from this data.
| Particular |
Marks of Statistics |
Marks of Elements of Accounts |
| Mean |
$60$ |
$62$ |
| Sum of the squares of the deviations taken from the mean |
$2870$ |
$2230$ |
| Sum of the products of the deviations taken from the mean |
$2409$ |
|
View full solution →The information regarding the price of a particular commodity and its supply is as follows:
$\bar{x}=35, \bar{y}=60, r=0.8, S_x=2.5$ and $S_y=2$
Obtain the regression line of $Y$ on $X$ from it.
View full solution →The following results are obtained for annual administrative expense and the profit of a company.
| Particulars |
$x$ |
$y$ |
| Mean |
$60$ |
$25$ |
| Standard deviation |
$6$ |
$3$ |
| Covariance |
$10.4$ |
|
View full solution →The following results are obtained while studying the annual income $($thousand $₹ )$ and annual saving $($thousand $₹)$ of a particular family. $\bar{y}=60$, variance of $X=144$, covariance $(x, y)=300$ and intercept $=-54$. Find the mean of $X$.
View full solution →The following results are obtained while studying the two related variables $X$ and $Y$. Obtain the regression line of $Y$ on $X$ from it.
$n=10, \Sigma x y=17880, \Sigma x=300, \bar{y}=50$ and $S_x=12$
If $X=40$ find $\hat{y}$.
View full solution →Answer the following questions from the given data.
$(i)$ If $b_{y x}=0.8, u=x-10, v=y+15$ then find the value of $b_{v i r}$.
$(ii)$ If $u=\frac{x-5}{3}, v=\frac{y-8}{5}$ and $b_{v u}=0.54$ then find the value of $b_{y x}$.
$(iii)$ If $u=5(x-40), v=\frac{y-50}{10}$ and $b_{y x}=0.25$ then find the value of $b_{ v }$.
View full solution →The regression line of $Y$ on $X$ is $6 x+8 y-64=0$ and the variance of $Y$ is $4$ times of the variance of $X$. If the value of $X$ changes by $4$ units, what will be the effect on the value of $Y\ ?$ Also find $R^2$ and interpret it.
View full solution →If the regression line of $Y$ on $X$ is $\hat{y}=38+2 x, \operatorname{Cov}(x, y)=32$ and variance of $Y=100$, find coefficient of determination and interpret it.
View full solution →If the regression line of $Y$ on $X$ is $\hat{y}=50-0.6 x$ and one of the observations used in fitting of the line is $(15,41)$, find the error for the estimated value and what can be concluded from this error ?
View full solution →The following data is obtained while studying the relation between the price $X(₹)$ and the supply $Y ($tons$)$ of an item for the past $100$ days. Obtain the regression line of the supply on the price from it and also estimate the supply if the price of an item is $₹ 18$.
| Particulars |
Price $x(₹)$ |
Supply $y ($ton$)$ |
| Mean |
$12$ |
$2.6$ |
| Standard deviation |
$1.6$ |
$4$ |
| Sum of the products of the deviations taken from the mean |
View full solution →The following results are obtained for a bivariate data.
| Particulars |
$x$ |
$y$ |
| Mean |
$200$ |
$260$ |
| Variance |
$144$ |
$36$ |
| Correlation Coefficient |
$-0.9$ |
View full solution →The information regarding the investment $X ($in crore $₹)$ made by a company in the stock market and its market value $Y ($in crore $₹)$ after two years is as follows. Estimate the market value after two years from this data, if $55$ crore $₹$ are invested in a particular year.
| Particulars |
Investment $x ($crore $₹)$ |
Value after $2$ year $y ($crore $₹)$ |
| Mean |
$50$ |
$60$ |
| Variance |
$121$ |
$361$ |
| Co-variance |
$100$ |
View full solution →Obtain the regression line of $Y$ on $X$ from the following data and find the estimated value of $Y$ when $X=2.5$.
$n=15, \Sigma x=35, \Sigma y=10, \Sigma x^2=760 \text { and } \Sigma x y=434$
View full solution →Obtain the regression line of height of wife on the height of husband from the data given for the height of husband $X ($in $cm )$ and the height of wife $Y ($in $cm).$
| Height of husband $x(cm)$ |
$172$ |
$168$ |
$170$ |
$165$ |
$167$ |
$164$ |
| Height of wife $y(cm)$ |
$170$ |
$167$ |
$170$ |
$166$ |
$165$ |
$162$ |
View full solution →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.
View full solution →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 $x (10\ kg)$ |
$10$ |
$16$ |
$10$ |
$12$ |
$17$ |
$18$ |
$14$ |
View full solution →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 $250\ kg$. View full solution →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 $X=7$.
View full solution →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$)$ |
$1.7$ |
$1.8$ |
$1$ |
$1$ |
$2.32$ |
$1.9$ |
$2$ |
View full solution →