Question

The table below gives the age and bone density for five randomly selected women. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting a woman's bone density based on her age. 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. Age 34 45 48 60 65 Bone Density 357 341 331 329 325 Table

  

Find the estimated slope. Round your answer to three decimal places.

Find the estimated y-intercept. Round your answer to three decimal places.

tep 3 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 4 of 6: Determine the value of the dependent variable ˆy at x = 0.

Step 5 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable ˆy is given by?

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

Answer 1

Solution:

Perform

regression in R use lm function.

coefficient function to get slope and y intercept

Rcode:

Age <- c(34, 45 ,48, 60, 65 )
Bone_Density <- c(357 ,341 ,331 ,329 ,325 )
regline <- lm(Bone_Density ~ Age)
coefficients(regline)
summary(regline)

Output:

Find the estimated slope

SLOPE=-0.964

Find the estimated y-intercept. Round your answer to three decimal places.

Y INTERCEPT=385.180

Step 3 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false

TRUE

Step 4 of 6: Determine the value of the dependent variable ˆy at x = 0.

we have

Bonedensity= 385.180 -0.964*age

when x=age=0

Bonedensity= 385.180 -0.964*0

Bonedenisty= 385.180

Step 5 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable ˆy is given by?

its the slope

the value of the independent variable is increased by one unit, then the change in the dependent variable ˆy is given by

slope=-0.964

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

R sq=0.8586 from output

=0.859

0.859