Correlation and Regression MCQs

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Topic Notes: Correlation and Regression

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131

In the linear regression equation Y = a + bX, what does the constant 'a' represent?

132

What is the standard formula for calculating the Spearman's rank correlation coefficient for non-tied data?

A $$\frac{{6\sum {D^2}}}{{N\left( {{N^3} - N} \right)}}$$ B $$1 - \frac{{\sum {D^2}}}{{{N^3} - N}}$$ C $$1 - \frac{{6\sum {D^2}}}{{N\left( {{N^2} - 1} \right)}}$$ D $$1 + \frac{{6\sum {D^2}}}{{N\left( {{N^3} - N} \right)}}$$

133

What is the formula for Spearman's rank correlation coefficient when tied ranks are present in the dataset?

A $$1 - \frac{{\frac{1}{2}\left[ {\left( {{m^3} - m} \right) + \frac{1}{2}\left( {{m^3} - m} \right) + .....} \right]}}{{{N^3} - N}}$$ B None of the above C $$1 - \frac{{\left[ {6\sum {D^2} + \frac{1}{2}\left( {{m^2} - m} \right) + \frac{1}{2}\left( {{m^2} - m} \right) + .....} \right]}}{{{N^3} - N}}$$ D $$1 - \frac{{6\left[ {\sum {D^2} + \frac{1}{{12}}\left( {{m^3} - {m_1}} \right) + \frac{1}{{12}}\left( {{m^3} - {m_2}} \right) + .....} \right]}}{{{N^3} - N}}$$

134

In the context of regression analysis, what is the nature of the relationship assumed to exist between the dependent variable and the independent variable?

135

Identify the false statement regarding regression and correlation analysis.

A Correlation coefficient is the geometric mean of the two regression coefficients B Coefficient of correlation is independent of origin but not of scale C The signs of the regression coefficients are always the same D The co-variance between two variables divided by the product of their standard deviations produces the value of coefficient of correlation

136

If the sum of two variables X and Y remains constant for all observations, what is the coefficient of correlation between them?

137

Determine the type of correlation between the two variates X (1, 2, 3, 4, 5, 6) and Y (10, 12, 14, 16, 18, 20).

138

Given Σx = 440, Σy = 330, Σx² = 17,986, Σy² = 10,366, Σxy = 13,467, and n = 11, what is the Pearson correlation coefficient (r) rounded to two decimal places?

139

What term describes a functional relationship between two variables?

140

What are the primary applications or utilities of correlation analysis in business and research?

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