Question

The table below gives the birth weights of five randomly selected mothers and the birth weights of their babies. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the birth weight of a baby based on the mother's birth weight. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

X: Mother 5.3 6.3 8 8.1 8.8

Y: Baby 5.1 5.4 7.1 8.2 8.9

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Determine the value of the dependent variable yˆ at x=0.

Step 4 of 6: Find the estimated value of y when x=8.1. Round your answer to three decimal places.

Step 5 of 6: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Step 1 of 6:

Regression equation is given as: y = a + b*x

The slope b can be calculated as follows:

The estimated slope = 1.107

Step 2 of 6:

The y-intercept can be calcualted as follows:

The estimated y-intercept = -1.144

Step 3 of 6:

Regression question can be written as follows:

y = -1.144 + 1.107*x

At x = 0, we get

y = -1.144 + 1.107*)

y = -1.144

Step 4 of 6:

Regression question can be written as follows:

y= -1.144 + 1.107*x

At x = 8.1, we get

y = -1.144 + 1.107*8.1

y = 7.823

Step 5 of 6:

All points predicted by the linear model fall on the same line: True

Step 6 of 6:

r = 0.9574

Coefficient of Determination = r2 = 0.95742

Coefficient of Determination = 0.917