Alex puts his spare change in a jar every single night. If he has $11.09 at the end of January, $22.27 at the end of Febuary, $44.35 in April, $77.82 in July, $89 in August, and $114.76 at the end...

Alex puts his spare change in a jar every single night. If he has $11.09 at the end of January, $22.27 at the end of Febuary, $44.35 in April, $77.82 in July, $89 in August, and $114.76 at the end of October perform a linear regression on this data to complete the following items.

1. What does the value of the correlation of the coefficient tell you about the correlation of the data?

2. Write the equation of the best-fitting line. ( Round to neartest thousandths )

3. On average how much money does Alex add to the jar each month?

4. Alex wants to buy a video game console at the end of December for $140. Will he have enough for his purchase? Show how you got the answer.

Asked on by anorth12

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steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, babybutch,

I am assuming you can use a TI graphing calculator on this.  First, you would make each month its relative number.  For example, January = 1, February = 2, March = 3, and so on.  Given that, you would have various points you can plot:

(1,11.09)

(2,22.27)

(4,44.35)

(7,77.32)

(8,89)

(10, 114.76)

Then, these numbers get plugged into the TI calculator.  Using a TI 83 Silver Edition, you press the STAT button, then press enter (selecting "Edit").  Make sure all the elements are clear in the columns (put the cursor on the title, press CLEAR, then put the cursor back down).  You can put all the x's in L1 and all the y's in L2.  Finally, press 2nd and the MODE button. 

Next, you need to make sure your statistic variables are on.  Press 2nd then the zero button, opening up the CATALOG.  Scroll down to the "DiagnosticOn" and press enter, then press enter again.

Now, press the STAT button, arrow over once to the CALC menu, then select 4, the linear regression.  You should see "LinReg(ax+b)" in the screen.  Then, you press 2nd and 1, then the comma button, then 2nd and 2, then press enter.  You should see the variables come up filling in the linear regression equation and the correlation coefficient.

For the first question, the correlation coefficient is r=0.9995.  That tells us that the linear regression model is a very, very, very good approximation of the situation going on.

For the second question, filling in the variables, we have y = 11.374x + -0.860.

For the third question, that would be the slope of the equation.  Alex looks to add about $11.37 into the jar each month.

And, finally, for December, x = 12.  Plugging that into the equation, we would have y = 11.374(12) + -0.860 = 135.628.  Or, Alex would have about $135.63 in the jar, not enough to purchase the video game.

I hope this helps, babybutch.  Good luck.

Steve

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anorth12 | Student, Grade 11 | (Level 1) Honors

Posted on

Very impormative and helped me understand how the question was solved.

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