Outliers · Exercise 20

The following are advertised sale prices of color televisions at Anderson’s:

\begin{array}{|c|c|}\hline \text{Size (inches)} & \text{Sale Price ($)} \\ \hline \text{9} & \text{147} \\ \hline \text{20} & \text{197} \\ \hline \text{27} & \text{297} \\ \hline \text{31} & \text{447} \\ \hline \text{35} & \text{1,177} \\ \hline \text{40} & \text{2,177} \\ \hline \text{60} & \text{2,497} \\ \hline\end{array}

(a) Decide which variable should be the independent variable and which should be the dependent variable.
(b) Draw a scatter plot of the data.
(c) Does it appear from inspection that there is a relationship between the variables? Why or why not?
(d) Calculate the least-squares line. Put the equation in the form ŷ = a + bx.
(e) Find the correlation coefficient. Is it significant?
(f) Find the estimated sale price for a 32-inch television. Find the cost for a 50-inch television.
(g) Does it appear that a line is the best way to fit the data? Why or why not?
(h) Are there any outliers in the data?
(i) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Statistics · §12.5 Outliers · Exercise 20