Please help with prject

Question

Project

MAT 115

Due: April 4^th , 2023

                             

 A study on 50 student regarding # of hours they study Mathematics per week versus their test scores is given at the table below:

# of hours study	Test scores
2	47
2	72
3	70
1.5	50
2	62
1.75	70
3	80
3	65
3	70
3	72
2	55
2.5	50
2.5	70
3	72
3	70
3	78
3	80
4	80
4	85
3	70
4	85
3	59
4	80
3	85
3	80
5	75
2	70
2	60
3.5	90

 

 

 

# of hours study	Test scores
3	92
4	90
3.5	45
5	90
3	80
3	85
3	70
4	85
3	72
2	60
2	90
2.5	72
3	60
3	59
4	70
3	75
4	80
3	80
3.5	85
3	80
3	73

 

Find / Draw then describe the following:

Linear Modeling

1.    The Scatter diagram then make an assumption based on possible predicted line’s slope.

2.   Find the predicted linear equation 𝑦=𝑚𝑥+𝑏 , where “x” is the number of hours students’ study Math per week and the “y” is students’ test scores.

3.   Interpret the slope of the predicted line you have found based on the content (study time versus students’ test scores).

4.   Identify how many hours a student should study per week, so then he/she can score at least 90 on his/her test.

5.   Do you think this predicted line can be used as the model to forecast students’ test scores in general, why or why not?

6.   Write a paragraph to describe your experience of doing this data analysis using at least 50 words. You may add opinions/suggestions/examples to demonstrate your experience.

 

       

 

 

Good luck!

Answer 1

Use desmos,

Google "desmos" and select the graphing calculator.

In the upper left side of the screen, you'll see a plus symbol. Click that and click "table". This will give you a table to enter all your data in. Do so. Put the "number of hours" in the x₁ column and put the "test scores" in the y₁ column.

Once you enter in all the data, go through every line a second time to make sure you typed the data in correctly. One mistake will affect your results.

Once the data is in correctly, you can see the scatter plot on the right screen. You might have to zoom out to see it.

To get the best fit line that models the data, click the plus in the upper left corner again and when a new box pops up, click in it and type in the equation:

y₁ ~ mx₁ + b

This is the same as y = mx + b except "y₁" instead of "y" and "x₁" instead of "x" and "~" instead of "=". This tells desmos you want the use the "x₁" and "y₁" values from your table and it tells desmos you want to come up with the best possible fit instead of being exactly equal. To get "x₁" you type "x" then "underscore" then "1". You must use a "cursor right" to get out of the underscore.

Once you have the equation in, desmos will give you the values of "m" and "b" that make the best-fit line and you will be able to view the best-fit line on the right screen intermixed with your data points.