Question
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?
The correct answer is
Linear regression
To determine the most appropriate statistical method to model the relationship between annual rainfall and the number of plant species, we need to consider the patterns shown in the graph.
- The graph displays a scatter plot where the X-axis represents annual rainfall and the Y-axis represents the number of plant species.
- The pattern in the graph shows a clear increasing trend, indicating that as the annual rainfall increases, the number of plant species tends to increase linearly.
- The most appropriate statistical method to model a linear relationship between two continuous variables (in this case, annual rainfall and number of plant species) is Linear Regression.
Explanation of why other options are incorrect:
- Kruskal-Wallis test: This is a non-parametric method used to compare more than two groups, not suitable for modeling relationships.
- Student’s t-test: Used to compare the means of two groups, but not for modeling relationships between continuous variables.
- Chi-squared test: Used for categorical data to test the association between variables, not applicable to continuous data shown in this graph.
Thus, the correct choice is Linear Regression.
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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 - 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 : - In __________ distribution, the Mode is found to be higher than mean.
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