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Find the equation of the regression line for the given data. Then construct a sc

ID: 3201119 • Letter: F

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 give 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 = 160 calories b) x = 90 calories c) x = 140 calories d) x = 50 calories (a) Predict the value y for x = 160. Choose the correct answer below. a. 435,000 b. 395,000 c. 215,000

Explanation / Answer

Regression equation formula
y = b0 + b1x
where,
y = estimated value of sodium
b0= y intercept of estimated regression line
b1=the slope of the estimated regression line
x= value of caloric content
slope and y intercept formula
b1= (x-x ) (y-y )/ (x-x )^2
b0 =y –b1( x )
x= value of the caloric
y=value of the sodium
x = mean value of the caloric (independent variable )
y =mean value of the sodium (dependent variable)

x = 150+180+120+130+70+190 /6
=840/6
x =140
y = 410+460+330+360+280+530/6
=2370/6
y =395


Cont…
S.no   caloric   sodium   (x-x )   (y-y )   (x-x )(y-y )   (x-x )^2
1   150   410   10   15   150   100
2   180   460   40   65   2600   1600
3   120   330   -20   -65   1300   400
4   130   360   -10   -35   350   100
5   70   280   -70   -115   8050   4900
6   190   530   50   135   6750   2500
                     
             Total    19200   9600

Sub all values in slope and y intercept , to find the value of b1 and b0

b1 =19200/9600
b1 =2
b0 = 395 – 2 (140)
b0=395-280
b0=115

now we predict the value of y , given x value here is 160
this value in to y = b0 + b1x
y = 115+2(160)
y=115+320
y=435
So , predicted value of y is 435.

Place all value in scatter plot
X= caloric
Y=sodium
  

Scatter plot. Line equation is y = 115+2x.

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