For which value of the correlation coefficient $(r),$ the regression coefficient becomes zero $?$
- A$1$
- B$-1$
- C$ 11$
- ✓$0$
Answer: D.
View full solution →Question types
LINEAR REGRASSION question types
180 questions across 6 question groups — pick any mix to generate a Statistics paper with step-by-step answer keys.
180
Questions
6
Question groups
5
Question types
01
MCQ
23 Q→021 Marks Each
29 Q→032 Marks Each
37 Q→043 Marks Each
48 Q→054 Marks Each
12 Q→065 Mark Each
31 Q→Sample Questions
LINEAR REGRASSION questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Which of the following is a regression line of $Y$ on $X$ ?
- A$\hat{y}=a+b x+c x^2$
- B$\hat{x}=c+b y$
- ✓$\hat{y}=a+b x$
- D$\hat{y}=a+b x^2$
Answer: C.
View full solution →Which regression line is used if the sale of a commodity depends on its advertisement cost ?
- ARegression line of advertisement cost on sale
- BRegression line of advertisement cost on advertisement cost
- ✓Regression line of sales on advertisement cost
- DRegression line of sales on sales
Answer: C.
View full solution →What is error e in estimation in case of line of regression of $Y$ on $X ?$
- ✓$y – ŷ$
- B$x̂ – ŷ$
- C$x – x̂$
- D$ŷ – x̂$
Answer: A.
View full solution →The regression line always passes which point ?
- ✓$(x̄, ȳ)$
- B$(0, ȳ)$
- C$(x̄, 0)$
- D$(0, 0)$
Answer: A.
View full solution →Will the regression co-efficient change if the values of both the variables are doubled with the help of transformation of scale ?
What is the value of error if a sample point is on the fitted line ?
The regression co-efficient is not independent of which transformation ?
The regression co-efficient is independent of which transformation ?
Give the name of a method to obtain the best fitted regression line.
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 $X.$
View full solution →$n=10, \bar{x}=40, \bar{y}=175, s_{x}=12, \operatorname{Cov}(x, y)=360$
Obtain the regression line of yield $Y$ on rainfall $X.$
If $u=5(x-40), v=2(y-18)$ and $b_{y x}=1.6$, find the value of $b_{v u} .$
View full solution →If $u=10(x-4.5), v=\frac{y-50}{10}$ and $b_{y x}=0.25$, find the value of $b_{v u}$.
View full solution →If $u=\frac{x-5}{3}, v=\frac{y-8}{5}$ and $b_{y x}=0.9$, find the value of $b_{v u}$.
View full solution →If $b_{y x}=0.85, u=x-15$ and $v=y-20$, find the value of $b_{v u}$.
View full solution →To study the relation between two variables, yearly income $(X)$ of a family and their yearly investment $(Y)$ in mutual funds, the following information is shown for a sample of $100$ families of a city.$X =$ Annual income of a family $($lakh $₹) y =$ Annual investment in mutual fund of a family $($thousand $₹)\bar{x}=5.5, \bar{y}=40.5, s_{x}=1.2, s_{y}=12.8, r=0.65$ Obtain the regression line of annual investment in mutual fund of a family on their annual income. Estimate the annual investment in mutual fund of a family whose annual income is $₹ 4.5$ lakh.
View full solution →If $\bar{x}=60, \bar{y}=75$ and $s_{x}^{2}: \operatorname{Cov}(x, y)=5: 3$, obtain the regression line of $Y$ on $X$ and estimate $y$ for $X=65$ from it.
View full solution →If $\bar{x}=5, \bar{y}=11$ and $b=1.2$, obtain the regression line of $Y$ on $X$.
View full solution →The following information is obtained for monthly advertisement cost and the sales of the last year for a company providing online shopping:
Obtain the regression line of the sales on the advertisement cost.
Obtain the regression line of the sales on the advertisement cost.
If $\bar{x}=30, \bar{y}=50, r =0.8$ and the standard deviations of $X$ and $Y$ are $2$ and $5$ respectively obtain the regression line of $Y$ on $X.$
View full solution →From the data and calculation of illustration $12$ of the chapter of linear correlation, obtain the regression line of profit on the sales. Estimate the profit when sales is $₹ 3$ crore.
View full solution →For the data given in illustration $I,$ obtain the regression line of maintenance cost $(Y)$ on the life of cars $(X)$ by using short-cut method.
View full solution →$(i)$ If the regression line is $\hat{y}=\frac{x}{2}+5$ and $s_{y}: s_{x}=5: 8$, find the coefficient of determination.
$(ii)$ If the regression line of $Y$ on $X$ is $4 x+5 y-65=0$, find the value of regression coefficient $b$.
View full solution →$(ii)$ If the regression line of $Y$ on $X$ is $4 x+5 y-65=0$, find the value of regression coefficient $b$.
$(i)$ If the regression line of $Y$ on $X$ is $\hat{y}=25+3 x$ and $\operatorname{Cov}(x, y)=48$, find the standard deviation of $X$. Also find coefficient of determination if the standard deviation of $Y$ is $15.$
$(ii)$ For the regression line given in the above question, how many units should be increased in the value of $X$ to increase approximately $15$ units in $Y ?$
View full solution →$(ii)$ For the regression line given in the above question, how many units should be increased in the value of $X$ to increase approximately $15$ units in $Y ?$
Six pairs of father-son are selected in a sample of an experiment to know the relation between the heights of fathers in cm $(X)$ and the heights of their adult sons in em $(Y).$ The following results are obtained from it.$\Sigma x=1020, \Sigma y=990, \Sigma(x-170)^{2}=60, \Sigma(y-165)^{2}=105$ $\Sigma(x-170)(y-165)=45$ Obtain the regression line of the heights of sons $(Y)$ on the heights of fathers $(X).$ Also verify the reliability of the regression model.
View full solution →A sample of seven students is taken from the students coming from abroad in the current year to study in university of the Gujarat State. The information regarding their $I.Q.$ and the marks obtained in an examination of $75$ marks is given below.
Obtain the regression line of $Y$ on $X$ and estimate the marks of a student whose $LQ.$ is $120.$ Also find the error in estimation when $1.0.$ is $100.$
View full solution →Obtain the regression line of $Y$ on $X$ and estimate the marks of a student whose $LQ.$ is $120.$ Also find the error in estimation when $1.0.$ is $100.$
In order to determine the relationship between monthly income $($in thousand $₹)$ and monthly expenditure $($in thousand $₹)$ of people of a group, a sample of seven persons is taken from that group and the following information is obtained.
Obtain the regression line of monthly expenditure on monthly income. If a person of the group has monthly income of $₹ 75$ thousand, estimate his monthly expenditure.
View full solution →Obtain the regression line of monthly expenditure on monthly income. If a person of the group has monthly income of $₹ 75$ thousand, estimate his monthly expenditure.
In order to study the relationship between the repairing time of accident damaged cars and the cost of repair, the following information is collected.
Obtain the regression line of $Y ($repairing cost$)$ on $X ($repairing time$).$ If the time taken to repair a car is $50$ hours, find an estimate of the repairing cost.
View full solution →Obtain the regression line of $Y ($repairing cost$)$ on $X ($repairing time$).$ If the time taken to repair a car is $50$ hours, find an estimate of the repairing cost.
The monthly sale of different types of laptops $($in hundred units$)$ and its profit $($in lakh $₹)$ for the last six months for a company is given below.
Obtain the regression line of $Y$ on $X.$ Also find the error in estimating $Y$ for $X = 7.$
View full solution →Obtain the regression line of $Y$ on $X.$ Also find the error in estimating $Y$ for $X = 7.$
In order to study the relationship between the density of population and the number of persons suffering from skin diseases, the following information is obtained for six cities regarding their density of population $($per sq. km$)$ and persons suffering from skin diseases $($per thousand$).$
Obtain the regression line of $Y$ on $X$ Estimate the number of patients suffering from skin diseases if density of population ofa city is $15000 ($per sq.km$).$ Examine the reliability of this regression model.
View full solution →Obtain the regression line of $Y$ on $X$ Estimate the number of patients suffering from skin diseases if density of population ofa city is $15000 ($per sq.km$).$ Examine the reliability of this regression model.
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