Question

In: Statistics and Probability

Use the following information to answer the next exercises. The cost of a leading liquid laundry...

Use the following information to answer the next exercises. The cost of a leading liquid laundry detergent in different sizes is given in Table 12.31.

size (ounces) cost ($) cost per ounce
16 3.99
32 4.99
64 5.99
200 10.99
  1. Using “size” as the independent variable and “cost” as the dependent variable, draw a scatter plot.
  2. Does it appear from inspection that there is a relationship between the variables? Why or why not?
  3. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx
  4. Find the correlation coefficient. Is it significant?
  5. If the laundry detergent were sold in a 40-ounce size, find the estimated cost.
  6. If the laundry detergent were sold in a 90-ounce size, find the estimated cost.
  7. Does it appear that a line is the best way to fit the data? Why or why not?
  8. Are there any outliers in the given data?
  9. Is the least-squares line valid for predicting what a 300-ounce size of the laundry detergent would you cost? Why or why not?
  10. What is the slope of the least-squares (best-fit) line? Interpret the slope.

Solutions

Expert Solution

a) scatter plot is given below

b) Yes there is a strong relationship between the variables. As you can see in the above scatter plot almost all points lie on the line.

c)

The least square line is

d)

The correlation coefficient between the variables is 0.9985. Yes it is significant.There is strong correlation between the variables.

g) As you can see in the graph below that the line of observed cost and predicted cost coincides. So it best fits the data.

h) there are no outliers you can see in the graph .

orchestra answered 1 year ago
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