Sample QuestionsLinear Regression (p-2) questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$b_{x y} \cdot b_{y x}=$ _________
- A
- B
$y _{ x }$
- ✓
$r ^2$
- D
$\left(y_y\right)^2$
Answer: C.
View full solution →- A
Regression coefficient of Y on X
- B
Regression coefficient of X on Y
- ✓
Correlation coefficient between X and Y
- D
Covariance between X and Y
Answer: C.
View full solution →$b_{y x}$ is ________
- ✓
Regression coefficient of Y on X
- B
Regression coefficient of X on Y
- C
Correlation coefficient between X and Y
- D
Covariance between X and Y
Answer: A.
View full solution →$b_{y x}$is ________
- A
Regression coefficient of Y on X
- ✓
Regression coefficient of X on Y
- C
Correlation coefficient between X and Y
- D
Covariance between X and Y
Answer: B.
View full solution →In the regression equation of X on Y
- A
X is independent and Y is dependent
- ✓
Y is independent and X is dependent
- C
Both X and Y are independent
- D
Both X and Y are dependent
Answer: B.
View full solution →If $u = x – a$ and $v = y – b$ then $r_{xy} = r_{uv}.$
View full solution →If $u = x – a$ and $v = y – b$ then $b_{xy} = b_{uv}.$
View full solution →$b_{yx}$ is the correlation coefficient between $X$ and $Y$.
View full solution →‘r’ is the regression coefficient of Y on X.
$b_{xy}$_ and $b_{yx}$_ are independent of change of origin and scale.
View full solution →If $b_{yx} > 1$ then $b_{xy}$_ is ______
View full solution →$|b_{xy} + b_{yx}| \geq $ ______
View full solution →If $\mathrm{u}=\frac{x-a}{c}$ and $\mathrm{v}=\frac{y-b}{d}$ then $\mathrm{b}_{\mathrm{yx}}=$ ______
View full solution →If $\mathrm{u}=\frac{x-a}{c}$ and $\mathrm{v}=\frac{y-b}{d}$ then $\mathrm{b}_{\mathrm{xy}}=$
View full solution →$Corr (x_1 – x) $= ______
View full solution →Find the line of regression of $\mathrm{X}$ on $\mathrm{Y}$ for the following data: $\mathrm{n}=8, \Sigma\left(\mathrm{x}_i-\mathrm{x}\right)^2=36, \Sigma\left(\mathrm{y}_i-\mathrm{y}\right)^2=44, \Sigma\left(\mathrm{x}_{\mathrm{i}}-\mathrm{x}\right)\left(\mathrm{y}_{\mathrm{i}}-\mathrm{y}\right)=24$
View full solution →If for a bivariate data $\bar{x}=10, \bar{y}=12, \mathrm{v}(\mathrm{x})=9, \sigma_{\mathrm{y}}=4$ and $\mathrm{r}=0.6$. Estimate $\mathrm{y}$ when $\mathrm{x}=5$.
View full solution →The regression equation of y on $x$ is given by $3x + 2y – 26 = 0$. Find $b_{yx}.$
View full solution →If $b_{yx} = -0.6$ and $b_{xy} = -0.216$ then find correlation coefficient between $X$ and $Y$ comment on it.
View full solution →\begin{align}
\text { For a bivariate data } \bar{x}=53, \bar{y}=28, \mathrm{~b}_{\mathrm{yx}}=-1.5 \text { and } \mathrm{b}_{\mathrm{xy}}=-0.2 \text {. Estimate } \mathrm{Y} \text { when } \mathrm{X}=50 \text {. }
\end{align}
Find the equation of line regression of $Y$ on $X$ for the following data:
$
\mathrm{n}=8, \Sigma\left(\mathrm{x}_{\mathrm{i}}-\bar{x}\right)\left(\mathrm{y}_{\mathrm{i}}-\bar{y}\right)=120, \bar{x}=20, \bar{y}=36, \sigma_{\mathrm{x}}=2, \sigma_{\mathrm{y}}=3 .
$
View full solution →(i) If for a bivariate data $b_{y x}=-1.2$ and $b_{x y}=-0.3$ then find $r$.
(ii) From the two regression equations $\mathrm{y}=4 \mathrm{x}-5$ and $3 \mathrm{x}=2 \mathrm{y}+5$, find $\bar{x}$ and $\bar{y}$.
View full solution →The following result was obtained from records of age (X) and systolic blood pressure (Y) of a group of 10 men.| | X | Y |
| MEAN | 50 | 140 |
| VARIANCE | 160 | 165 |
and $\Sigma\left(x_i-\bar{x}\right)\left(y_i-\bar{x}\right)=1120$. Find the Prediction of blood pressure of a man of age 40 years. View full solution →The equation of two regression lines are $2 x+3 y-6=0$ and $3 x+2 y-12=0$ Find (i) Correlation coefficient (ii) $\frac{\sigma_x}{\sigma_y}$
View full solution →For bivariate data, the regression coefficient of Y on X is 0.4 and the regression coefficient of X on Y is 0.9. Find the value of the variance of Y if the variance of X is 9.
Identify the regression equations of x on y and y on x from the following equations.
2x + 3y = 6 and 5x + 7y – 12 = 0
In partially destroyed record, the following data are available variance of X = 25. Regression equation of Y on X is 5y – x = 22 and Regression equation of X on Y is 64x – 45y = 22 Find
(i) Mean values of X and Y.
(ii) Standard deviation of Y.
(iii) Coefficient of correlation between X and Y.
The equation of two regression lines are $x-4 y=5$ and $16 y-x=64$. Find means of $X$ and $\mathrm{Y}$. Also, find the correlation coefficient between $\mathrm{X}$ and $\mathrm{Y}$.
View full solution →For 50 students of a class, the regression equation of marks in statistics $(\mathrm{X})$ on the marks in Accountancy $(Y)$ is $3 y-5 x+180=0$. The mean marks in accountancy is 44 and the variance of marks in statistics $\left(\frac{9}{16}\right)^{\text {th }}$ of the variance of marks in accountancy. Find the mean in statistics and the correlation coefficient between marks in two subjects.
View full solution →In a partially destroyed laboratory record of an analysis of regression data, the following data are legible:
Variance of X = 9
Regression equations:
8x – 10y + 66 = 0 And 40x – 18y = 214.
Find on the basis of the above information
(i) The mean values of X and Y.
(ii) Correlation coefficient between X and Y.
(iii) Standard deviation of Y.
The equation of the two lines of regression are 3x + 2y – 26 = 0 and 6x + y – 31 = 0. Find
(i) Means of X and Y
(ii) Correlation coefficient between X on Y
(iii) Estimate of Y for X = 2
(iv) var (X) if var (Y) = 36
The equation of the line of regression of $y$ on $x$ is $v=\frac{2}{9} x$ and $x$ on $y$ is $x=\frac{y}{2}+\frac{7}{6}$. Find (i) $\mathrm{r}$ (ii) $\sigma_y^2$ if $\sigma_x^2=4$.
View full solution →The equations of two regression lines are $10 x-4 y=80$ and $10 y-9 x=-40$ Find:
(i) $\bar{x}$ and $y$
(ii) $b_{y x}$ and $b_{x y}$
(iii) If $\operatorname{var}(Y)=36$, obtain $\operatorname{var}(X)$
(iv) $\mathrm{r}$
View full solution →For certain X and Y series, which are correlated the two lines of regression are 10y = 3x + 170 and 5x + 70 = 6y. Find the correlation coefficient between them. Find the mean values of X and Y.
Two lines of regression are $10 x+3 y-62=0$ and $6 x+5 y-50=0$ Identify the regression equation equation of $x$ on $y$. Hence find $\bar{x}, \bar{y}$, and $\mathrm{r}$.
View full solution →The data obtained on X, the length of time in weeks that a promotional project has been in progress at a small business, and Y the percentage increase in weekly sales over the period just prior to the beginning of the campaign.
| X | 1 | 2 | 3 | 4 | 1 | 3 | 1 | 2 | 3 | 4 | 2 | 4 |
| Y | 10 | 10 | 18 | 20 | 11 | 15 | 12 | 15 | 17 | 19 | 13 | 16 |
Find the equation of regression line to predict percentage increase in sales if the company has been in progress for 1.5 weeks.
If the two regression lines for a bivariate data are $2 x=y+15(x$ on $y)$ and $4 y-3 x+25(y$ on $x$ ) find
(i) $\bar{x}$
(ii) $\bar{y}$
(iii) $b_{y x}$
(iv) $b_{x y}$
(v) $r$ [Given $\sqrt{ } 0.375=0.61$ ]
View full solution →The two regression lines between height (X) in includes and weight (Y) in kgs of girls are 4y – 15x + 500 = 0 and 20x – 3y – 900 = 0. Find the mean height and weight of the group. Also, estimate the weight of a girl whose height is 70 inches.
Regression equation of two series are $2 x-y-15=0$ and $4 y+25=0$ and $3 x-4 y+25=0$. Find $\bar{x}, \bar{y}$ and regression coefficients, Also find coefficients of correlation. [Given $\sqrt{ } 0.375=$ $0.61]$
View full solution →\begin{align}
\text { The two regression equation are } 5 x-6 y+90=0 \text { and } 15 x-8 y-130=0 \text {. Find } \bar{x}, \bar{y}, r \text {. }
\end{align}