Outliers · Exercise 18

The cost of a leading liquid laundry detergent in different sizes is given in.
\begin{array}{|c|c|c|}\hline \text{Size (ounces)} & \text{Cost ($)} & \text{Cost per Ounce} \\ \hline \text{16} & \text{3.99} & \\ \hline \text{32} & \text{4.99} & \\ \hline \text{64} & \text{5.99} & \\ \hline \text{200} & \text{10.99} & \\ \hline\end{array}

(a) Complete for the cost per ounce of the different sizes of laundry detergent.
(b) Using size as the independent variable and cost per ounce as the dependent variable, 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) If the laundry detergent were sold in a 40 oz. size, what is the estimated cost per ounce?
(g) If the laundry detergent were sold in a 90 oz. size, what is the estimated cost per ounce?
(h) Does it appear that a line is the best way to fit the data? Why or why not?
(i) Are there any outliers in the the data?
(j) Is the least-squares line valid for predicting what a 300 oz. size of the laundry detergent would cost per ounce? Why or why not?
(k) What is the slope of the least-squares (best-fit) line? Interpret the slope.

OpenStax, Statistics · §12.5 Outliers · Exercise 18