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which of the following statements is incorrect? for a linear regression model, when used to test hypothesis of correlations, the performance measure is estimated using its coefficient of determination when both predictor and response variables have mean 0, the intercept is zero when you fit a linear regression in the mathematical equation of linear

Question: Which Of The Following Statements Is Incorrect? For A Linear Regression Model, When Used To Test Hypothesis Of Correlations, The Performance Measure Is Estimated Using Its Coefficient Of Determination When Both Predictor And Response Variables Have Mean 0, The Intercept Is Zero When You Fit A Linear Regression In The Mathematical Equation Of Linear

Which of the following statements is incorrect?

For a linear regression model, when used to test hypothesis of correlations, the performance measure is estimated using its coefficient of determination

When both predictor and response variables have mean 0, the intercept is zero when you fit a linear regression

In the mathematical equation of Linear Regression Y = β1 + β2X + ϵ, (β1, β2) refers to as Y-intercept and slope respectively

In practice, line of best fit or regression line is found when sum of squared distance from the points to the regression line is maximum

Answer 1

The incorrect statement among the options provided is:

"In practice, line of best fit or regression line is found when sum of squared distance from the points to the regression line is maximum."

This statement is incorrect because the line of best fit or regression line is actually found when the sum of the squared distances from the points to the regression line is minimized, not maximized. This is known as the principle of least squares.

To find the line of best fit, the goal is to minimize the residuals, which are the differences between the observed values and the predicted values on the regression line. The regression line is fitted in such a way that the sum of the squared residuals is as small as possible. This ensures that the line is as close as possible to the actual data points.

By minimizing the sum of squared residuals, we are finding the line that best represents the relationship between the predictor variable(s) and the response variable. This line can then be used for making predictions and testing hypotheses about the correlation between the variables.

In summary, the correct statement is that the line of best fit or regression line is found when the sum of squared distances from the points to the regression line is minimized, not maximized.