SOLUTION: Hours Studied: 1, 3, 3, 4, 4, 2 Test Score : 70, 80, 85, 90, 85, 75 The table shows the number of hours students studied and their score on a math test in Ms.

Algebra ->  Probability-and-statistics -> SOLUTION: Hours Studied: 1, 3, 3, 4, 4, 2 Test Score : 70, 80, 85, 90, 85, 75 The table shows the number of hours students studied and their score on a math test in Ms.       Log On


   

Question 1136359: Hours Studied: 1, 3, 3, 4, 4, 2
Test Score : 70, 80, 85, 90, 85, 75
The table shows the number of hours
students studied and their score on a
math test in Ms. Aduke’s class.
Write an equation for the trend line.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
basically, you plot the points and then draw a straight line that minimizes the distnce from that straight line to all the points.

there is software that does that for you, but you can also eyeball the graph and get reasonably close to what the software would have generated.

here's my eyeball estimate.

$$$

i looked at the graph and drew a straight line that i felt was closest to all the points on the graph.

i then took two points on the line in the graph to make my equation.

the points i chose were (1,72) and (4,88).

the slope of the line was (88 - 72) / (4 - 1) = 16 / 3 = 5.33 rounded to two dedcimal places.

the slope intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept.

the equation became y = 5.33 * x + b

i then took one of the points on the line that i previously chose to make the slope to find the y-intercept.

the point i chose was (1,72).

i replace y with 72 and x with 1 to get 72 = 5.33 * 1 + b

i then solved for b to get b = 72 - 5.33 = 66.67.

the y-intercept was 66.67 and the equation became y = 5.33 * x + 6.67.

here's what the software generated.

$$$

the equation from the software is y = 63.90243902439 + 5.9756097560976x

when displayed in descending order of degree, the equation becomes:

y = 5.9756097560976 * x + 63.90243902439

i compawred what the software gave me to what i created manmually.

here's the two equations.

software generated is y = 5.98 * x + 63.90 rounded to 2 decimal places.

manually generated is y = 5.33 * x + 66.67 rounded to 2 decimal places.

i then graphed both of these equations on the same graph to see how much they differed from each other.

here's what the graph looks like.

$$$

the software generated line is in red.

the manually generated line is in blue.

if you have the software generator, that is preferable.

if not, then manually generated will have to do.

the software generated one that i used can be found at http://www.alcula.com/calculators/statistics/linear-regression/








Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

1.  Go to the site

    https://www.socscistatistics.com/tests/regression/Default.aspx



2.  Read the description attentively (it takes 2-3 minutes to understand everything).



3.  Input your data; then press the "CALCULATE" button.



4.  Get your trend equation in the form

    y = 5.97561*X + 63.90244

That is all.

Solved, answered and completed.