For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient are x̅ = 1.0, y̅ = 2.0, s x= 3.0, s y= 9.0, r = 0.8 Then the regression line of y on x is:
y = 2 + 2.4(x - 1)
The y-on-x slope is r(sy/sx)=0.8(9/3)=2.4. The line passes through (x̄,ȳ)=(1,2), so y−2=2.4(x−1), or y=2+2.4(x−1).
Similar Questions
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Important Questions from Regression Analysis
- Using linear regression (least squares), the best-fit line for the given dataset is $y = 2.2x + 2.3$. Given the residual sum of squares is 25.8, the coefficient of determination ($r^2$), is ______________ . (rounded off to two decimal places)
$x$ 2 3 4 5 $y$ 8 9 7 16 - Given the pairs of values of $(X, Y)$ as $(2, 60)$, $(4, 70)$ and $(6, 90)$, $m$ is the slope of the linear regression plot of $Y$ on $X$. The value of $m$ is _______.
- The data given in the table are fitted to the equation $y = mx$ using the method of least squares. The value of $m$ is ______ (rounded off to one decimal place).
$x$ 1 2 3 4 $y$ 2 6 7 10 The graph below shows a plot of annual rainfall on the X axis and number of plant species on the Y axis. Based on the pattern in the graph, which one of the following statistical methods would be most appropriate to model the relationship between annual rainfall and the number of plant species?
- Arrange the following steps of formulating research proposal in a logical sequential order :
(i) Defining research problem.
(ii) Formulation of hypothesis.
(iii) Review of literature.
(iv) Collection of data.
(v) Research Design.
Choose the correct answer from the options given below :
