Question

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

Size (ounces)	Cost ($)
16	3.69
32	4.89
64	5.39
200	10.29

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

ŷ = a + bx.

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

r =  
If the laundry detergent were sold in a 40-ounce size, find the estimated cost per ounce. (Use your equation from part (d). Round your answer to two decimal places.)

$  per oz

Part (g)

If the laundry detergent were sold in an 88-ounce size, find the estimated cost per ounce. (Use your equation from part (d). Round your answer to two decimal places.)
$  per oz

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

Answer 1

Here we have given that

X : Size (ounces)

Y : Cost ($)

Size (ounces )(X)	Cost ($)(Y)
16	3.69
32	4.89
64	5.39
200	10.29

(A)

First we find the sample correlation coefficient r

Now we find the sums

n=number of observations=4

= 16+32+64+200=312

= 3.69+4.89+5.39+10.29=24.26

X	Y	X^2	Y^2
16	3.69	256	13.62
32	4.89	1024	23.91
64	5.39	4096	29.05
200	10.29	40000	105.88

we get

=256+1024+4096+40000=45376

=13.62+23.91+29.05+105.88=172.46

X	Y	XY
16	3.69	59.04
32	4.89	156.48
64	5.39	344.96
200	10.29	2058

we get

= 59.04+156.48+344.96+2058=2618.48

Now, we get the sample correrlation coefficient r

=

=0.9948

The correlation coefficient is 0.9948

(B)

Now,we want to find the least square regression equation.

Now we can find the regression coefficients

=

=0.0345

Now we find  

we get,

= 6.07 - (0.0345)*78

=3.379

the least square regression line

= 3.379 + 0.0345 X

(C)

here slope of the least square best-fit line is 0.0345

(D)

X: 88 ounce size

now we want find the estimated cost per ounce

the least square regression line

= 3.379 + 0.0345*(88)

=6.42

the estimated cost per ounce is 6.42