Suppose that you performed a Simple Linear Regression of Height (equal the y-variable) on Weight (equal...

Suppose that you performed a Simple Linear Regression of Height (equal the y-variable) on Weight (equal the x-variable). If the calculated r-value was equal to 0.9575, which of the following statements are appropriate parts of the interpretation of this r-value? Choose ALL that apply.

	A.	Given that the r-value is 0.9575, the r-squared value will be 0.9785, rounded off to the 4th decimal place.
	B.	Since this r-value is a positive number, the estimated y-intercept will also be a positive number because the sign of r and the sign of the y-intercept are always the same.
	C.	Since this r-value is a positive number, the linear relationship between Height and Weight is positive.
	D.	Because this r-value is so close to 1.00, it appears that Height and Weight have a strong linear relationship.

Expert Solution

Here in this scenario we performed a Simple Linear Regression of Height (equal the y-variable) dependent variable on Weight (equal the x-variable) independent variable. If the calculated r-value was equal to 0.9575, the following statements are appropriate parts of the interpretation of this r-value.

A) it is not correct.

Explanation : if the correlation coefficient is 0.9575 then the r square coefficient of determination value is 0.9162, . which is indicated that there is 91.62% variablity in y dependent variable explained by x variable.

B) it is not correct.

Explanation : in Regression model when the correlation coefficient is Positive then it need not to be y intercept Positive. It can be negative in some sichuations. The sign of r and y intercept are not always same. Only thing is when the correlation coefficient is positive then slope of Regression is positive. Slope of Regression equation and correlation coefficient signs are same.

C) this is correct.

Explanation : Since this r-value is a positive number, the linear relationship between Height and Weight is Positive. When the value of height of person is goes up then value of weight is also goes up. Since it is positively correlated.

D) this is Correct.

Explanation : Because this r-value is so close to 1.00, it appears that Height and Weight have a strong linear Positive relationship. If the value of r is close to 0 then there is week correlation between them. If the value of r is negative then the correlation between them is negative they negatively correlated in this case the value of slope is also negative.

So Only Option C and D are correct.

Thank you.

orchestra answered 1 year ago

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