Question

What is the equation of the line of best fit for the following data? Round the slope and y-intercept of the line to three decimal places. x y 4 17 6 12 8 9 11 4 13 3 A. y = 22.105x - 1.560 B. y = 1.560x - 22.105 C. y = -22.105x + 1.560 D. y = -1.560x + 22.105

Answer 1

The table of data is shown below

The equation of line best fit is given in the form $y=mx+b$

to find the slope 'm', follow these steps:

STEP 1
$Mean (X) = \frac{4+6+8+13+11}{5}=8.4$
$Mean(Y)= \frac{17+12+9+4+3}{5}=9$

STEP 2
Refer to Picture 2 and Picture 3 for the working out of $( x_{i} -mean(X))$ and $( y_{i} -mean(Y))$
$( x_{i}-X)( y_{i}-Y) =(-4.4)(8)+(-2.4)(3)+(-0.4)(0)+(2.6)(-5)$$+(4.6)(-6)$
$( x_{i}-X)( y_{i}-Y)$=(-35.2)+(-7.2)+0+(-13)+(-27.6)=-83

STEP 3:
$( x_{i}-X) ^{2}$ = $(-4.4)^{2}+ (-2.4)^{2}+ (-0.4)^{2}+ (2.6)^{2}+ (4.6)^{2}=53.2$

STEP 4:
To find slope, divide answer in STEP 2 by the answer in STEP 3
$m= \frac{-83}{53.2} =-1.56$

STEP 5:
$b=Mean(Y)-[slope*mean(X)]$
$b=9-(-1.56*8.4)=22.105$

We have the slope, $m=-1.56$ and y-intercept of 22.105
The equation of line is
$y=22.105-1.560x$

Correct answer: Last statement 

Answer 2

The equation of the line which best fit for the provided data (the slope and y-intercept of the line to three decimal places) is,

$y=-1.560x+22.105$

What is the equation of line?

The equation of the line is the way of representation of a line in the equation form.

It can be given as,

$y=mx+c$

Here, (m) is the slope of the line and (c) is the y intercept.

The equitation of the lines represents the line by the set of points on which the line lies or passes through in the coordinate system.

The table given in the problem is,

x       y

4      17

6      12

8      9

11      4

13      3

The mean value of the x is,

$M_x=\dfrac{4+6+8+11+13}{5}\\M_x=8.4$

The mean value of the y is,

$M_y=\dfrac{17+12+9+4+3}{5}\\M_y=9$

By the regression line calculator we find the slope of the given data is ,

$m=-1.56$

This indicates the stiffness and the direction of the line for the table data.

The y intercept of the given table by the regression line calculator can be find out as,

$c=22.105$

Putting the above in the equation of line, we get,

$y=-1.560x+22.105$

Thus the equation of the line of best fit for the following data is,

$y=-1.560x+22.105$

Learn more about the equation of line here;

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