LASA 1: Linear Regression

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mat_106_m3a2_lasa_guidelines.docx

MAT 106 Some notes, guidelines, and a sample report for the Module 3 LASA

Please note that this assignment requires that our report be in the form of a narrative. (Even without this specification, let’s get into the habit of always completing our LASA math assignments in a narrative format.) This means that your final report should read like an essay or a magazine article. Your LASA reports must not look like a math homework assignment. That is, even though there are seven items to address, we should not explicitly identify these items as “1 through 7” in our report.

Please be sure to use full sentences, and do your best to avoid grammatical, spelling, and usage errors. Assume that the people reading your report understand basic math, but are not familiar with linear regression.

At this time, please bring up M3 Assignment 2 in the left-side menu of our eClassroom. Click on the second blue link in the assignment’s instructions. You’ll get a spreadsheet that contains four pairs of numbers. This is just meaningless sample data that comes with this LASA; it’s not the “real” data that we’re going to use in our actual reports. But let me use this sample data to write a sample LASA. Pretend that the graph of this sample data is not yet available to us, and let’s do items 2 – 8 of the ten-step Excel procedure (given in the assignment’s instructions) to produce a graph for your four pairs of numbers.

Now, pretend that your four pairs of numbers are data from a study that wanted to find the correlation between the average number of hours that a basketball team practiced each day and the number of wins that the team achieved that year. So the variables are “average number of practice hours each day” and “number of wins”.

Your completed data analysis reveals that r = 1.00 . From this, we can calculate the Pearson correlation, r , by r = , and we find that r = 1.00 .

If the trendline of a graph has an upward slope (like the right half of the letter “V”), then there is a positive correlation between the two variables. And if the trendline has a downward slope (like the left half of “V”), then the variables are negatively correlated.

Please note that your graph can be copied and pasted directly into your MS Word LASA report. Please do this. Right-click the top of your graph (near the words “Chart Title”) to copy it. You can then paste it into your report. After pasting, double-click on the words “Chart Title” and give your graph an appropriate name. Now that your graph is in your report, there’s no longer any need to hand in your Excel spreadsheet – just close your spreadsheet and don’t submit it. Pasting your graph into your Word report and submitting just one Word report is preferable to submitting a Word report plus a separate Excel document.

Also, please give your final report an appropriate title.

On the next page, you’ll find a sample report that uses the graph that you just made.

Practice Makes Perfect – A Basketball Statistical Study John Akutagawa

We conducted a study to determine a correlation between basketball teams’ practice times and their corresponding numbers of season wins. For each of the four teams in Argosy’s intramural hoops league, we recorded the average number of hours that a team practiced each day and the number of wins that the team achieved during the season.

Our results are shown in the following graph.

When we analyzed the data, we found that the square of the Pearson correlation was r = 1.00 , and that the Pearson correlation itself was r = 1.00 . A correlation (r-value) of 1.00 is the strongest correlation possible; in fact, 1.00 is a perfect correlation. This result means that a basketball team’s effectiveness is very strongly correlated to the amount of time that it spends practicing.

Our graph shows that this correlation is a positive one. This means that the more a team practices, the more it wins.

A formula relating practice time and number of wins can be expressed as w = 5p , where p is the average number of hours that a team practices each day and w is the number of wins it can expect to achieve during the season.

We know from statistical theory that correlation does not imply causality. So the question remains: is there a causal relationship between practice time and team wins? Based on common sense, it seems reasonable to conclude that the answer to this questions is yes. Of course, other variables (such as talent and luck) also affect a team’s win total. However, our final conclusion is that increased practice time does indeed result in more wins.

Practice time versus number of wins

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