The table shows the numbers x of absences in a school year and the final exam scores y of several students

Question

The table shows the numbers x of absences in a school year and the final exam scores y of several students

Absences, x	4	5	6	1	1
Final Exam Score, y	82	80	75	91	90

Absences, x	7	0	2	5	6
Final Exam Score, y	73	94	88	79	76

QUESTIONS	ANSWERS
a. Use technology to find an equation of the line of best fit. Round the slope and y-intercept to the nearest integer.	The line of best fit is _________.
b. Interpret the slope and y-intercept of the line of best fit.	The slope is ________  and the y-intercept is _______. So, a student with 0 absences is expected to earn a ______  on the final exam, and the score decreases by about ________ points per absence.
c. Approximate the final exam score of a student who has 3 absences.	about ______  points

Answer 1

Open desmos. If you google it, under the desmos search return, click "graphing calculator".

You'll get a page that has a black header bar across the top with "desmos" written in white, a large x-y graph on the right, and an empty space on the left. In the upper right corner, under the black header bar, you will see a plus symbol. If you hover over that plus symbol, it will say "Add Item". Click that plus symbol then in the downselect options, click "table". This will give you a place to enter your data. The header will say x₁ and y₁. Enter your data by typing in all the x-values (Absences) in the x₁ column and the corresponding y-values (Final Exam Score) in the y₁ column. It will look like this:

Once the data is entered, you will use the desmos to calculate the line of best fit. Remember that the equation for a line is "y = mx + b" where "m" is the slope of the line and "b" is the y-intercept of the line. but in this case, you will need to tell desmos to use the values in your table in the y₁ column as the y-values in the calculation of the best-fit line. And you will need to again tell desmos to use the values in your table in the x₁ column as the x-values in the calculation of the best-fit line. To do that, you will need to use the equation of a line "y₁ = mx₁ + b" BUT you do not actually want the y₁ to equal the "mx₁ + b", you just want it to be the best possible fit. To do that you will use the equation "y₁ ~ mx₁ + b". That tells desmos to find the best possible line that is as close to "equals" as possible.

So, to do that, click the plus symbol in the upper left corner of the page again. This time in the downselection, click "f(x) expression". This will give you a new block to type in your equation "y₁ ~ mx₁ + b". To do so, type the "y" then to get the "y₁" hit the underscore key "shift dash" (this is the key on your keyboard next to the zero) then type "1" and you should see "y1" in your "f(x) expression" block. Next you MUST click the cursor right button to get out of the "y1". Then hit the squiggle" (~) key which is just left of the number 1 on your keyboard (usually requires a shift to get the ~). Then type "m" and then "x₁" (again, type "x" then "underscore" then "1" then "cursor right"). Finally type +b.

When you finish, you will get this:

This result tells you the equation of the line. You can switch back to just plain "x" and "y" when you write it. It will be y = -2.9697x + 93.7879

Remember that "m" is the slope and "b" is the y-intercept. The negative in front of the slope means it is decreasing meaning for every absence, a person's test score is expected to go down about 3 points.

If you want to estimate a test result, plug in a certain number of absences (x) into your equation. But round off your answer because this is just an estimate,

You will be able to look at the graph if you scroll out on the graph section of your webpage.

Answer 2

Answer 3

Hi Autumn, For part a), I used an online calculator (https://www.socscistatistics.com/tests/regression/default.aspx). You can find plenty of them online, or you can use Excel for it. The line of best fit is y = -2.9697x + 93.78788 The slope is -2.9697 and the y-intercept is 93.78788. So a student is 0 absences is expected to earn a 94 on the exam (I rounded 93.78788), and the score decreases by about 3 points (I rounded 2.9697) per absence. If a student has 3 absences, he will get -3(3) + 94 = 85 on the exam. I hope this helps!

Answer 4

I used https://www.graphpad.com/quickcalcs/linear2/. You can use a calculator or another online tool.

The line of best fit is y = -2.97x + 93.79

The slope is -2.97 and the y intercept is 93.79.

A student with 0 absences is expected to earn a 93.79. The score decreased by about 2.97 points per absence.

A student with 3 absences will have a final exam score of about y = -2.97(3) + 93.79 = about 90.88 or 91 if rounded to a whole number.