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. 215,000Explanation / 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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