Question

Which linear regression equation best fits the given points?

(0,4), (1,4), (2,5), (3,6), (4,6), (5,6), (5,7), (6,7)




yˆ= 1/2x − 1

yˆ= −1/2x + 4

yˆ= −1/2x

yˆ= 1/2x + 4

Answer 1

You have to know how to enter this into your calculator.  Step by step: hit the stat button and then edit.  Enter your x values one at a time in the first column, hitting enter after each value.  When finished with x's, arrow over to the second column and enter each y value in, one at a time, hitting enter after each value.  When you're done, hit stat again, tab over to calc and hit enter.  You will then arrow down to LinReg(ax+b).  Hit enter.  If you have a TI 83, then the equation should just generate automatically.  If you have a TI84 family, you need to arrow down to "calculate" and then hit enter.  Your equation will then generate.  It is the last choice above, y = 1/2x + 4.  Learn how to use your calculator; it can do SO many cool things for you!!!

Answer 2

Option D is the correct answer, yˆ= (1/2)x + 4 .

What is linear regression ?

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables).

Calculate the mean of the x -values and the mean of the y -values.

X' = (X₁ + X₂+..........+Xₐ)/a

Y'= (Y₁+Y₂+..............+Yₐ)/a

The following formula gives the slope of the line of best fit:

$\rm m = \dfrac{\sum (X_{a}-X')(Y_{a}-Y')}{\sum (X_{a}-X')^{2}}$

Compute the y -intercept of the line by using the formula:

Y' - mX' = b

Y'= 5.625

X' = 3.25

m = 0.562

Y' - mX' = b

5.625-0.562  *3.25 = 3.7985 = b

yˆ= (1/2) x + 4

best fits the for the given points .

Therefore Option D is the correct answer.

To know more about linear regression .

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