Question

A random sample of beef hotdogs was taken and the amount of sodium (in mg) and calories were measured. ("Data hotdogs," 2013) The data are in table #10.1.11. Create a scatter plot and find a regression equation between amount of calories and amount of sodium. Then use the regression equation to find the amount of sodium a beef hotdog has if it is 170 calories and if it is 120 calories. Which sodium level that you calculated do you think is closer to the true sodium level? Why?

Table #10.1.11: Calories and Sodium Levels in Beef Hotdogs

Calories: 186, 181, 176, 149, 184, 190, 158, 139, 175, 148, 152, 111, 141, 153, 190,157, 131, 149, 135, 132

Sodium: 495, 477, 425, 322, 482, 587, 370, 322, 479, 375, 330, 300, 386, 401, 645,440, 317, 319, 298, 253

Answer 1

X - Amount of calories. Y - Amount of sodium

SCATTER PLOT

Sum of X = 3137
Sum of Y = 8023
Mean X = 156.85
Mean Y = 401.15
Sum of squares (SS_X) = 9740.55
Sum of products (SP) = 39091.45

Regression Equation = y = bX + a

b = SP/SS_X = 39091.45/9740.55 = 4.01327

a = M_Y - bM_X = 401.15 - (4.01*156.85) = -228.33129

y = 4.01327X - 228.33129

Now for  x= 170 . y = 4.01327 * 170 - 228.33129 = 453.92

Now for  x= 120 . y = 4.01327 * 120 - 228.33129 = 253.26

I think sodium level calculated for 170 calories is closer to the true sodium level because as we see the scatter plot, we have less data ( almost no) data near 120 calories but near 170 calories we have more data ( at least more than 120 calories ) so the calculated sodium level for 170 calories can be more accurate than 120 calories.

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