10.5 practice residuals and coefficient of determination

The correlation coefficient, r is used to determine

• y values given values of x.

• x values given values of y.

• the strength and direction of relationship between x and y.

• none of these.

Tags

CCSS.HSS.ID.C.8

The correlation coefficient

• is the same as r².

• can never be negative.

• is the square of coefficient of determination.

• is the square root of coefficient of determination.

Answer explanation

We use the r² to get the coefficient of determination!

Tags

CCSS.HSS.ID.C.8

Coefficient of correlation lies between

• 0 and +1

• 0 and -1

• -1 and +1

• -5 and +5

Answer explanation

The value of r must be between -1 and +1

Tags

CCSS.HSS.ID.C.8

What is the coefficient of determination for the data characteristics shown?

• -.928

• .928

• .861

• -.861

Tags

CCSS.HSS.ID.C.8

A study compared the number of years of education and a person's annual salary. The correlation coefficient of the data was r = 0.913. What is the coefficient of determination?

• 0.834

• 0.887

• 0.457

• 0.913

Tags

CCSS.HSS.ID.C.8

If the coefficient of determination is 0.81, the correlation of coefficient is

• 0.6561.

• must be positive.

• must be negative.

• could be either +0.9 or -0.9.

Answer explanation

Correlation of coefficient is the square root of coefficient of determination.

Tags

CCSS.HSS.ID.C.8

As shown in the table, a person's target heart rate during exercise changes as the person gets older. Use the graphing calculator to find the coefficient of determination.

• -0.999

• -0.664

• 0.998

• 1.503

Tags

CCSS.HSS.ID.C.8

The correlation between two variables is r=0.5. Which of the statement is correct?

• Average values of y changes by 0.5 when x is increased by 1.

• Average values of x changes by 0.5 when y is increased by 1.

• x explains 25% of the variation in y.

• y explains 25% of the variation in x.

Answer explanation

The variation in y can be explained by the variation in x.

Tags

CCSS.HSS.ID.B.6B

If the correlation coefficient r between blood pressure and weight is 0.7,

• it is a moderate positive relationship.

• 49% of the variation in weight can be explained by the variation in the blood pressure.

• 51% of the variation in weight is due to other factors than the blood pressure.

• All of the above.

Answer explanation

Correlation coefficient of 0.7 indicates a moderate positive relationship. Using coefficient of determination (0.7)²=0.49 means 49% of the variation in Y can be explained by X. The remaining 51% of the variation in Y is unexplained or due to other factors.

Tags

CCSS.HSS.ID.B.5

If the coefficient of determination is 0.876, what percent of the variation is explained?

• 56%

• 88%

• -67%

• 92%

Tags

CCSS.HSS.ID.B.6B