Question

The cost of a leading liquid laundry detergent in different sizes is given below.

Size (ounces)	Cost ($)	Cost per ounce
16	3.69
32	4.59
64	5.89
200	10.39

Part A) Using "size" as the independent variable and "cost" as the dependent variable, make a scatter plot.

Part B) Does it appear from inspection that there is a relationship between the variables? Why or why not?

Part C) Calculate the least squares line. Put the equation in the form of: ŷ = a + bx. (Round your answers to three decimal places.)

Part D) Find the correlation coefficient r. (Round your answer to four decimal places.)

Part E) If the laundry detergent were sold in a 30-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)

Part F) If the laundry detergent were sold in an 86-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)

Part G) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)

Answer 1

The relevant R code is as follows:

# loading dataset
dataset <- data.frame(Size = c(16, 32, 64, 200), Cost = c(3.69, 4.59, 5.89, 10.39))

# making scatterplot
plot(x = dataset$Size, y = dataset$Cost, xlab = "Size", ylab = "Cost", main = "Scatterplot")
# seems to be a linear relationshipt with positive correlation

# calculating least squares line
(ls_line <- lm(formula = (dataset$Cost ~ dataset$Size)))
# regression line is y_hat = 3.377 + 0.035x

# finding correlation coefficient
(r <- cor(x = dataset$Size, y = dataset$Cost))
# correlation coefficient is r = 0.9974

# finding cost for 30 ounce size
(cost_est_30 <- (3.377 + 0.035 * 30))
# estimated cost is $4.43

# finding cost for 86 ounce size
(cost_est_86 <- (3.377 + 0.035 * 86))
# estimated cost is $6.39

# slope of the best fit line
(slope <- ls_line$coefficients[2])
# slope is 0.035