Step 1: Understanding correlation analysis.
In correlation analysis, the focus is on measuring the strength and direction of the linear relationship between two variables. Both variables are treated symmetrically since correlation does not specify which variable is dependent or independent.
Step 2: Analysis of options.
- (A) Are treated with distinction: This is incorrect. Both variables in correlation analysis are treated symmetrically.
- (B) Are treated differently based on individual characteristics: This is incorrect. In correlation analysis, both variables are treated the same.
- (C) Are treated symmetrically: This is correct. The correlation coefficient measures the strength and direction of the linear relationship between the two variables without distinguishing between them.
- (D) Are regressed: This is incorrect. Regression analysis is different from correlation analysis, as regression considers one variable as dependent and the other as independent.
Step 3: Conclusion.
The correct answer is (C), as correlation analysis treats both variables symmetrically.
Coefficient of determination measures
(A) Correlation between the dependent and independent variables.
(B) The residual sum of squares as a proportion of the total sum of squares.
(C) The explained sum of squares as a proportion of the total sum of squares.
(D) How well the sample regression fits the data.
Choose the correct answer from the options given below:
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: