In simple regression analysis, if the correlation coefficient is a positive value, then Select one:

A. the slope of the regression line must also be positive.

B. the least squares regression equation could have either a positive or a negative slope.

C. the y-intercept must also be a positive value.

D. the coefficient of determination can be either positive or negative, depending on the value of the slope.

E. the standard error of estimate can have either a positive or a negative value.

Question

03-12-2019
Mathematics

contestada

In simple regression analysis, if the correlation coefficient is a positive value, then Select one:

A. the slope of the regression line must also be positive.

B. the least squares regression equation could have either a positive or a negative slope.

C. the y-intercept must also be a positive value.

D. the coefficient of determination can be either positive or negative, depending on the value of the slope.

E. the standard error of estimate can have either a positive or a negative value.

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Diatonic254 Diatonic254 · Answer 1 · 2019-12-11T08:44:13+01:00

A

Simple linear regression is usually represented as a straight line graph showing the correlation between two variables. If the correlation coefficient is a positive value, then the slope of the regression line must also be positive.

Step-by-step explanation:

This is because the gradient of the line shows a relationship between the two variables (a change in y-axis (representing one variable) over the change in x-axis (representing the other variable)).

Gradient = Δy / Δx

A positive change in y / a positive change in x = a positive value. This means a positive increase in variable x causes a proportionate increase in variable y.

A negative change in y / a negative change in x = a positive value. This means a decrease in variable x causes a proportionate decrease in variable y.

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Parrain Parrain · Answer 2 · 2021-11-05T13:57:59+01:00

When using simple regression, if the correlation coefficient is a positive value, A. the slope of the regression line must also be positive.

The correlation coefficient shows the change in y as a result of a change in x. When this figure is positive, it means that the change in y is positive when there is a change in x.

This will then be represented graphically as a positive slope because the correlation coefficient is the mathematical representation of the slope.

In conclusion, the slope of a regression line will be positive when the correlation coefficient is positive.

Find out more at https://brainly.com/question/14228374.