Outliers · Exercise 15

The average number of people in a family who attended college for various years is given in.

$$\begin{array}{cc}\text{Year}& \text{No. of Family Members Attending College}\\ \text{1969}& \text{4.0}\\ \text{1973}& \text{3.6}\\ \text{1975}& \text{3.2}\\ \text{1979}& \text{3.0}\\ \text{1983}& \text{3.0}\\ \text{1988}& \text{3.0}\\ \text{1991}& \text{2.9}\end{array}$$

(a) Using year as the independent variable and number of family members attending college as the dependent variable, draw a scatter plot of the data.
(b) Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
(c) Does the y-intercept, a, have any meaning here?
(d) Find the correlation coefficient. Is it significant?
(e) Pick two years between 1969 and 1991 and find the estimated number of family members attending college.
(f) Based on the data in, is there a linear relationship between the year and the average number of family members attending college?
(g) Using the least-squares line, estimate the number of family members attending college for 1960 and 1995. Does the least-squares line give an accurate estimate for those years? Explain why or why not.
(h) Are there any outliers in the data?
(i) What is the estimated average number of family members attending college for 1986? Does the least-squares line give an accurate estimate for that year? Explain why or why not.
(j) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Statistics · §12.5 Outliers · Exercise 15