Determine True or False 1. A positive residual indicates the regression line und

Question

Determine True or False

1. A positive residual indicates the regression line underpredicted the y value

2. r has the same sigh as the slope of the regression line

3. If r is close to +/- 1, one may use the regression line to predict y values for x values outsides those from the dataset used to construct the regression line

4. If the value of r for variables x and y is 0.46 and the x values are all multiplied by 1.5, the new value of r will be 0.69

5. The point containing the mean of the explanatory variable and the mean of the response variable is on the regression line

6. The units of r are the same as the units of the x variable

7. Summarizing the data will improe R^2

8. An outlier that is far off the regresssion line will always decrease r

Explanation / Answer

1. A positive residual indicates the regression line underpredicted the y value

Answer : Residual : Observed value - Predicted value

So  a positive residual indicates the regression line underpredicted the y value is true.

2. r has the same sigh as the slope of the regression line.

Answer : In both r and slope Sxy comes into numerator which can be positive or negative. So both r and slope has same sign.

It is true.

3. If r is close to +/- 1, one may use the regression line to predict y values for x values outsides those from the dataset used to construct the regression line.

If r is close to +/- 1 then it shows a very strong relationship between the variables. So one may use the regression line to predict y values for x values outsides those from the dataset used to construct the regression line. It is true.

4. If the value of r for variables x and y is 0.46 and the x values are all multiplied by 1.5, the new value of r will be 0.69.

Correlation remain unaffected by the scaling or change of units. So it is false.

5. The point containing the mean of the explanatory variable and the mean of the response variable is on the regression line.

It is true.

6. The units of r are the same as the units of the x variable.

r do not have unit. So it is false.

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