Question

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (Each pair of variables has a significant​ correlation.) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The caloric content and the sodium content​ (in milligrams) for 6 beef hot dogs are shown in the table below.

Calories, x	160	180	120	120	80	190		​(a) x=150 calories	​(b) x=100 calories
​Sodium, y	415	465	330	380	270	510		​(c) x=130 calories	​(d) x=200 calories

Answer 1

X	Y	XY	X²	Y²
160	415	66400	25600	172225
180	465	83700	32400	216225
120	330	39600	14400	108900
120	380	45600	14400	144400
80	270	21600	6400	72900
190	510	96900	36100	260100
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
850	2370	353800	129300	974750

Sample size, n =	6
x̅ = Ʃx/n =	141.667
y̅ = Ʃy/n =	395
SSxx = Ʃx² - (Ʃx)²/n =	8883.33
SSyy = Ʃy² - (Ʃy)²/n =	38600
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	18050

Slope, b = SSxy/SSxx =    2.031894934

y-intercept, a = y̅ -b* x̅ =    107.1482176

Regression equation :   

ŷ = 107.1482 + (2.0319) x  

Scatterplot:

a) Predicted value of y at x =150

ŷ = 107.1482 + (2.0319) * 150 = 411.9325

b) Predicted value of y at x = 100

ŷ = 107.1482 + (2.0319) * 100 = 310.3377  

c) Predicted value of y at x = 130

ŷ = 107.1482 + (2.0319) * 130 = 371.2946  

d) As X = 200 is outside the range of data of calories given in the sample we cannot calculate sodium