DC L.
asked • 06/15/20Use the regression line to calculate the values of y for x = 72 and x = 832.
Find the least-squares regression line for the data below.
x = 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000
y = 170, 320, 499, 601, 758, 921, 1001, 1107, 1290, 1350, 1424, 1528, 1633, 1750, 1810, 1991, 2017, 2120, 2223, 2465
Use the regression line to calculate the values of y for x = 72 and x = 832.
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2 Answers By Expert Tutors
Jon S. answered • 06/15/20
Tutor
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(6)
Patient and Knowledgeable Math and English Tutor
The equation of the regression line is
Y = 2.239*X + 173.3
Plug in x=72 and x=832 to get corresponding predicted values of Y.
DC L.
Thanks alot Jon.S I used an Linear Regression calculator to determined the equation for the regression line, but where I was really stuck at was how to go about using the regression line to calculate the values for x = 72 and x = 832. do I use an equation to determine?
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06/15/20
Roberto A. answered • 06/15/20
Tutor
New to Wyzant
Physics PhD student
The type of work you do depends on what your teacher/professor expects but regardless of the work, you essentially want to fit the data to a straight line, y=b1 x+b0. This means you need to calculate a slope, b1, and a y intercept, b0, using the given data. You can then just plug in x=72 and x=832.
If they want computational work then you can simply input the data into excel (or any software of your choice) and plot the data and fit to a line. Excel will just do the work for you.
If they want you to do it by hand then you need to find the individual means for the x data and the y data and then use the formulas for linear regression which are
b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]
b0 = y - b1 * x
where x and y are the x and y means respectively.
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Stephanie B.
Step 1: Using your graphing calculator, create a table of x and y values (use STAT - EDIT to enter x and y values). You can graph this data by turning on STAT PLOT on the calculator. You can see that it is approximately linear Step 2: Use STAT-CALC - LinReg to find the best-fit m and b for this line: I got m =2.24 and b = 173.3. You can save the best-fit equation in the calculator if you know how. Otherwise, just write down the m and b values, and then enter the equation y = 2.24x + 173.3 into your "Y=" editor. Then press 2nd - CALC -value. Then enter "72" and press enter, this gives you a Y-value of 334. Next, press 2nd - CALC - value. THen enter "832" and press enter, this gives you a Y-value of 2029. Note that you may be a little off from this, depending on how you do Step 2.06/15/20