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+b1xy^=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	3737	3939	4040	5050	6464
Bone Density	357357	347347	344344	343343	336336

Step 4 of 6:

Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^.

Step 6 of 6:

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

Answer 1

The regression equation is defined as,

From the data values,

	Age, X	Bone Density, Y	X^2	Y^2	X*Y
	37	357	1369	127449	13209
	39	347	1521	120409	13533
	40	344	1600	118336	13760
	50	343	2500	117649	17150
	64	336	4096	112896	21504
Sum	230	1727	11086	596739	79156

The least square estimate of intercept and slope are,

The regression equation is,

Step 4 of 6:

If the age is increased by one unit, then the bone density will decrease by 0.5652 (the slope coefficient gives the value for change in dependent variable for one unit change in independent variable)

Step 6 of 6:

The coefficient of determination value is obtained using the formula,

Where,