Question

The following table shows the number of students taking the AP Statistics examination (in thousands) for each year after 1997.

Year after 1997	0	5	6	7	8	9	10	11	12
Students (thousands)	7.5	49.8	58.2	65.9	76.8	88.2	98	108.2	116.9

If we use this data to create a least squares regression line to predict the number of students taking the AP Statistics examination for a given year, which of the following is the correct interpretation of the coefficient of determination?

(A)   99.8% of the variability in number of students taking the AP Statistics examination is explained by the linear relationship with year.

(B)    99.6% of the variability in number of students taking the AP Statistics examination is explained by the linear relationship with year.

(C)    99.8% of the variability in year is explained by the linear relationship with number of students taking the AP Statistics examination.

(D)   99.6% of the variability in year is explained by the linear relationship with number of students taking the AP Statistics examination.

(E)    There is a strong, positive, linear relationship between the number of students taking the AP Statistics examination and year.

Answer 1

The output is given below:

Here, the value of R² is 0.996...

Here,

Dependent Variable: Number of Students

Independent Variable: Year after 1997

As R² is 0.996, it means that 99.6% of the variations in the Dependent Variable is explained by the linear relationship with the Independent Variable...

Here,

The correct option is: Option B.

i.e. 99.6% of the variability in number of students taking the AP Statistics examination is explained by the linear relationship with year.

End of the Solution...