Question

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

Size (ounces)	Cost ($)
16	3.49
32	4.39
64	5.19
200	10.09

Calculate the least squares line. Put the equation in the form of:

ŷ = a + bx. (Round your answers to three decimal places.)

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

If the laundry detergent were sold in a 20-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)

If the laundry detergent were sold in an 80-ounce size, find the estimated cost. (Use your equation from part (c). Round your answer to two decimal places.)

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


Interpret the slope. (Round your answer to three decimal places.)

As the  ---Select--- number of ounces cost  of liquid laundry detergent increases by one unit, the detergent  ---Select--- size cost  increases by   ---Select--- ounces dollars

Answer 1

	Size (X)	Cost (Y)	X * Y	X2	Y2
	16	3.49	55.84	256	12.1801
	32	4.39	140.48	1024	19.2721
	64	5.19	332.16	4096	26.9361
	200	10.09	2018	40000	101.8081
Total	312	23.16	2546.48	45376	160.1964

Equation of regression line is Ŷ = a + bX


b = 0.035
a =( Σ Y - ( b * Σ X) ) / n
a =( 23.16 - ( 0.0352 * 312 ) ) / 4
a = 3.047
Equation of regression line becomes Ŷ = 3.0467 + 0.0352 X

r = 0.999

When X = 20
Ŷ = 3.047 + 0.035 X
Ŷ = 3.047 + ( 0.035 * 20 )
Ŷ = 3.75

When X = 80
Ŷ = 3.047 + 0.035 X
Ŷ = 3.047 + ( 0.035 * 80 )
Ŷ = 5.85

Slope  b = 0.035

Interpret slope

As the  number of ounces cost  of liquid laundry detergent increases by one unit, the detergent size cost  increases by $0.035 dollars.