Question

The following table shows the energy provided (in kilocalories) and the amount of carbohydrates (in grams) in a 100 ml bottle of sports drinks for six different brands. Use the dat. Carbohydrates (grams) 9.5 4 1 9 9 3 Energy (kilocalories) 21 37 22 18 25 28 Click the icon to view the correlation coefficient,r, for various values of n and a a) Determine the correlation coefficient between the amount of carbohydrates and the energy provided The correlation coeffichent between the amount of carbohydrates and the energy provided is (Type an integer or decimal rounded to three decimal places as needed) b) Determine whether a correlation exists at 0.05. Does a linear correlation exist when a = 0.05? O Alinear correlation exists. O Alinear correlation does not exist c) Determine the equation of the Ine of best it for the amount of carbohydrates and the energy provided The equation of the line of best it for the amount of carbohydrates and the energy providedisy (Use integers of decimals for any numbers in the expression. Round to three decimal places as needed) d) Use the equation in part (c) to estimate the amount of energy provided in a sports drink with 9 grams) of carbohydrates Using the equation in part (e) estimate the amount of energy provided in a sports drink with 9 gram(s) of carbohydrates is (Type an integer or decimal rounded to three decimal places as needed) Click to select your answer(s) kilocalories

Answer 1

Hi,

Consider,

Carbohydrates (gram): Independent variable

Amount of energy (kilocalories): Dependent variable

	Carbohydrates (gm) X	Energy (kilocalories) Y	X2	Y2	XY
	9.5	21	90.25	441	199.5
	4	37	16	1369	148
	1	22	1	484	22
	9	18	81	324	162
	9	25	81	625	225
	3	28	9	784	84
Σ	35.5	151	278.25	4027	840.5

> x= 35.5

5 x2 = 278.25

> y = 151

5 y2 = 4027

>xy = 840.5

a.

η(Σχy) - (Σκ) Σy) Correlation Coefficient = r = [η Σχ2 - (Σκ)2][nΣy2 – (Σy)2] = -0.425 (rounded to 3 decimal places)

The correlation coefficient between the amount of carbohydrates and energy produced is r = -0.425.

b.

Ho:p = 0

H: P 0

Irlyn-2 vip2 = 0.940

Reject Hift >ta/2n-2

ta/2.n-2 = 3.4954

Hence, we accept H.There is a not significant linear correlation between amount of carbohydrates and the energy.

So, the linear correlation does not exist.

c.

Equation of line best fit to the data is obtained by using the method of least-square.

ỹ = Botß1*x

ΣyΣ x?)- (Σχ)(Σxy). Intercept = Bo = η (Σx?)- (Σα)2 -= 29.757 (rounded to 3 decimal places)

n(Σχy) - (Σκ)(Σy). Slope = B1 = η(Σx2)- (Σκ)2 -= -0.776 (rounded to 3 decimal places)

y = 29.757 -0.776* x

d.

y = 29.757 -0.776 + 9 = 22.775

The estimated amount of energy provided in a sports drink with 9 gms of carbohydrates is 22.775 kilocalories.

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