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.

(a)x=180 (b)x=90

​(c)x=120

(d)x=50
Calories, x   Sodium, y
150   420
170   470
130   350
130   360
80 240
180   510

FIND THE REGRESSION EQUATION:

Answer 1

Let, x = Calories

and y = Sodium

Let us plot scatter plot with regression line using Excel.

600 Sr. No. xy 500 y= 2.687x+15.41 R=0.990 400 150 170 130 130 80 180 420 470 350 360 240 510 2350 63000 79900 45500 46800 19200 91800 346200 X^2 y^2 22500 176400 28900 220900 16900 122500 16900 129600 6400 57600 32400 260100 124000967100 300 Series1 5 -Linear (Series1) 6 Total 200 100 50 100 150 200 2 Sheet1 Sheet2 Sheet3 AR + eady

The equation of regression line is

y = 15.41 + 2.687.

i.e.

y = bo + b12

We use given values of x to predict y because the value of coefficient of determination $(R^{2})$ is 0.990. i.e. X explain 99% variation of y.

a)

I = 180

y = 15.41 + 2.687 * 180 = 499.07

b)

r=90

y = 15.41 +2.687 * 90 = 257.24

c)

r=120

y = 15.41 + 2.687 * 120 = 337.85

d)

y = 15.41 + 2.687 * 50 = 149.76