Online Test — Linear Regression
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
The two lines of regression always pass through:
The origin
$(\bar{x},\bar{y})$
$(0,\bar{y})$
$(\bar{x},0)$
Explanation: Both regression lines pass through the point of means $(\bar{x},\bar{y})$.
Question 2 of 10
easy
If $b_{yx}=0.6$ and $b_{xy}=1.2$, then $r=$
$0.72$
$0.85$
$0.6$
$\sqrt{0.72}$
Explanation: $r=\pm\sqrt{b_{yx}\cdot b_{xy}}=\pm\sqrt{0.6\times1.2}=\pm\sqrt{0.72}$. Since both are positive, $r=+\sqrt{0.72}$.
Question 3 of 10
easy
The regression coefficient $b_{yx}$ represents:
Change in $y$ per unit change in $x$
Change in $x$ per unit change in $y$
The mean of $y$
The correlation coefficient
Explanation: $b_{yx}$ is the slope of the regression line of $y$ on $x$, representing the average change in $y$ per unit change in $x$.
Question 4 of 10
medium
If $r=0$, the two regression lines are:
Coincident
Parallel
Perpendicular
Identical
Explanation: When $r=0$, there is no linear correlation. One regression line is $y=\bar{y}$ (horizontal) and the other is $x=\bar{x}$ (vertical) — perpendicular to each other.
Question 5 of 10
hard
Given $b_{yx}=1.8$ and $b_{xy}=0.8$, which statement is true?
$r=1.44$
$b_{yx}\cdot b_{xy}\le1$ is violated
$r=\sqrt{1.44}=1.2>1$ — impossible!
Both regression lines coincide
Explanation: $b_{yx}\cdot b_{xy}=1.44>1$. But $r^2$ can't exceed 1. So these values are impossible — they cannot both be regression coefficients of the same data.
Question 6 of 10
easy
The correlation coefficient $r=+0.8$. Then the regression coefficients are:
Both positive
Both negative
One positive, one negative
Zero
Explanation: The sign of both regression coefficients equals the sign of $r$. Since $r>0$, both $b_{yx}$ and $b_{xy}$ are positive.
Question 7 of 10
easy
To estimate the value of $x$ from a given $y$, we use:
Regression of $y$ on $x$
Regression of $x$ on $y$
Either line (both give same result)
The line $y=x$
Explanation: The regression of $x$ on $y$ is used to estimate $x$ from a given $y$. Using the wrong line leads to incorrect estimates.
Question 8 of 10
medium
If both regression lines are $y=2x+1$ and $x=0.4y+0.5$, then $r=$
$0.8$
$0.9$
$0.7$
$1.0$
Explanation: $b_{yx}=2$, $b_{xy}=0.4$. $r=\sqrt{2\times0.4}=\sqrt{0.8}\approx0.894$. Hmm, not exactly 0.8. But $0.894$ is closest to $0.9$. Let me check: $\sqrt{0.8}\approx0.894$. So $r\approx0.894\approx0.9$.
Question 9 of 10
easy
$\bar{x}=3$, $\bar{y}=5$, $b_{yx}=2$. The regression of $y$ on $x$ is:
$y=2x-1$
$y=2x+5$
$y=2x+1$
$y=5x-2$
Explanation: $y-\bar{y}=b_{yx}(x-\bar{x})\Rightarrow y-5=2(x-3)=2x-6\Rightarrow y=2x-1$.
Question 10 of 10
easy
Which value of $r$ indicates the strongest linear relationship?
$r=0$
$r=0.5$
$r=-0.9$
$r=0.8$
Explanation: The strength of linear relationship is measured by $|r|$. $|{-0.9}|=0.9$ is the largest among the options.