Find the equation of the line of best fit from the data in the table?

Question

Round the slope and the y-intercept to the nearest hundredth.

x | 2 | 4 | 6 | 8 | 10
_______________

y | 15 | 37 | 60 | 75 | 94


These are the possible answers I have to choose from..

y = 9x - 3
y= 10x - 3
y = 9.8x - 2.6
y = 9.2x - 2.1

The same for this one too..

x | 0 | 3 | 4 | 5 | 12
_____________________

y | 8 | 2 | 6 | 9 | 12


and the following choices are..

y = 0.53x + 4.88
y = 0.63x + 4.88
y = 0.73x + 4.98
y = 0.43x + 4.98

Answer 1

Well as you are not calculating the best line yourself how about plugging x values into each equation , calculating the predicted y value, then see which equation gives the least total amount of error

Answer 2

OK, the line of best fit can be found by the method of Least Squares. What "Least Squares" does is take the difference between the actual Y values at each X and subtract the calculated Y values at each X. That tells you how far the line is from the actual value. It then squares these values (to eliminate negatives) and minimizes the differences between the fit line and the actual Y values.

You can do this in a spreadsheet. In Excel, the verbs are Slope(y,x) and Intercept(y,x). So, put the values for x in one column and the values for y in the next column. Then in another cell type =Slope( then point to the top of the Y column and highlight to the bottom of the Y column; then type a comma and point to the top and highlight to the bottom of the X column and then type a close parenthesis. So the equation looks like this:: =SLOPE(C7:C11,B7:B11) if you put the Y's in C7 to C11 and the X's in B7 to B11. The value is 9.8. The same equation works for the intercept if you just change the word SLOPE to INTERCEPT. Clearly, from just the slope of 9.8 you can see which answer is correct.

But let's say you don't have a spreadsheet, how do you approach this problem? I would calculate the slope between each pair of X and Y values. Since slope is (y1-y2)/(x1-x2)
you would get these values: 11,11.5,7.5,9.5 now average them to get 9.875 since that is closest to y=9.8x-2.6 I would go with that answer.

Answer 3

Dont panic at all. Calculating the line of best fit (regression equation) is quite simple. After all the necessary computations, i found out that the CORRECT answer is
y=9.8x-2.6 or y= -2.6+9.8x. Remember the equation of line of best fit=a+bx.,a=intercept, b= slope and x= the variable you can use for prediction. And a is calculated using this formula- y bar (mean of y variabes)minus b*xbar( mean of x variables)
and b is calculated by this formula N sigmaXY minus sigmaX sigmaY divided by N sigmaXsquared minus sigma (X)squared. After you get the value of "a" using that formula and the value for "b" using that formula, replace them in the regression equation, you will see that the answer is -2.6+9.8x. First prepare a table showing these colunms
X, Y, XY and Xsquared and SUM up all the variables in each colunm and key inn the respective variables in the formula. Notice, there are 2 regression lines: X on Y and and the regression equation of Y on X,.which is the one we are calculating here. Am a Statistician by "birth". OK?

Answer 4

Plot the numbers on graph paper

draw a line that includes most points with the same number of points above and below the line

measure the slope. it should be 9, 10, 9.8 or 9.2

find the value of y where the line crosses the x axis. it should be -3, -2.6 or -2.1

the two numbers you select should give you one of the answers.

Answer 5

If you are using a TI-83+ calculator...

Type STAT,
Enter your x-values in L1
Enter your y-values in L2

Type STAT, CALC (arrow right), 4 (LinReg),
The equation is y = 9.8x - 2.6 for the first equation

Answer 6

y = 9.2x - 2.1

replace the first few values of x into the equation and u will obtain y

Answer 7

9.8x - 2.6 with a correlation of 0.9945