Question

Need help with parts C, D, E, F and J please and thank you!

ei The cost of a leading liquid laundry detergent in different sizes is given below. Size (ounces) Cost (5) 16 3.29 32 429 64 5.29 200 10.19 Part Parti Parte Call the last sein. Put the gation in the form of a bw. Round your answers to three decimal places) Part Find the correlation contr. (Round your answer to four decimal places) Is it can • Yes NO OPart (6) if the laundry detergent were sold in a 20 once wire, End the estimated cost. Use your equation from part). Round your awer to two decimal aces) $ Parton If the laundry detergent were sold in an once in the estimated cos(Use your ego from part) Round your awer to two decimal place)

Answer 1

(C)

The independent variable is SizeSize, and the dependent variable is CostCost. In order to compute the regression coefficients, the following table needs to be used:

	Size	Cost	Size*Cost	Size2	Cost2
	16	3.29	52.64	256	10.8241
	32	4.29	137.28	1024	18.4041
	64	5.29	338.56	4096	27.9841
	200	10.19	2038	40000	103.8361
Sum =	312	23.06	2566.48	45376	161.0484

Based on the above table, the following is calculated:

$\bar X = \frac{1}{n} \sum_{i=1}^{n} X_i = \frac{ 312}{ 4} = 78$

$\bar Y = \frac{1}{n} \sum_{i=1}^{n} Y_i = \frac{ 23.06}{ 4} = 5.765$

$SS_{XX} = \sum_{i=1}^{n} X_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right)^2 = 45376 - 312^2/4 = 21040$

$SS_{YY} = \sum_{i=1}^{n} Y_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} Y_i\right)^2 = 161.0484 - 23.06^2/4 = 28.1075$

SSXY = ΣX,Y, - (Σ) (Σ) = 2566.48 – 312 x 23.06/4 n 1=1 767,8

Therefore, based on the above calculations, the regression coefficients (the slope mm, and the y-intercept nn) are obtained as follows:

$m = \frac{SS_{XY}}{SS_{XX}} = \frac{ 767.8}{ 21040} = 0.0365$

$n = \bar Y - \bar X \cdot m = 5.765 - 78 \times 0.0365 = 2.9186$

Therefore, we find that the regression equation is:

Cost = 2.9186 + 0.0365 Size

Y=2.9186 + 0.0365 X

(D)

based on this information, the sample correlation coefficient is computed as follows

$r = \frac{ SS_{XY}}{\sqrt{ SS_{XX} SS_{YY}}} = \frac{ 767.8}{\sqrt{ 21040 \times 28.108}} = 0.998$

r=0.998

YES,significant.

(E)

We have :

Cost = 2.9186 + 0.0365 Size

When size=20 ounces

Cost=2.9186 + 0.0365*20

Cost=$ 3.6486

(F)

We have :

Cost = 2.9186 + 0.0365 Size

When size=80 ounces (its not clearly visible but i think its 80)

Cost=2.9186 + 0.0365*80

Cost=$ 5.8386

(J)

slope=0.0365

As the number of ounces of liquid laundary detergent increases by one unit,the detergent cost increases by 0.0365 dollars.

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