QuestionQuestion

Project 1

Instructions
For this assignment, collect data (BELOW) exhibiting a relatively linear trend, find the line of best fit, plot the data and the line, interpret the slope, and use the linear equation to make a prediction. Also, find r2 (coefficient of determination) and r (correlation coefficient). Discuss your findings. Your topic may be that is related to sports, your work, a hobby, or something you find interesting. If you choose, you may use the suggestions described below.
A Linear Model Example and Technology Tips are provided in separate documents.
Tasks for Linear Regression Model (LR)
(LR-1) Describe your topic, provide your data, and cite your source. Collect at least 8 data points. Label appropriately
(LR-2) Plot the points (x, y) to obtain a scatterplot. Use an appropriate scale on the horizontal and vertical axes and be sure to label carefully. Visually judge whether the data points exhibit a relatively linear trend. (If so, proceed. If not, try a different topic or data set.)
(LR-3) Find the line of best fit (regression line) and graph it on the scatterplot. State the equation of the line.
(LR-4) State the slope of the line of best fit. Carefully interpret the meaning of the slope in a sentence or two.
(LR-5) Find and state the value of r², the coefficient of determination, and r, the correlation coefficient. Discuss your findings in a few sentences. Is r positive or negative? Why? Is a line a good curve to fit to this data? Why or why not? Is the linear relationship very strong, moderately strong, weak, or nonexistent?
(LR-6) Choose a value of interest and use the line of best fit to make an estimate or prediction. Show calculation work.
(LR-7) Write a brief narrative of a paragraph or two. Summarize your findings and be sure to mention any aspect of the linear model project (topic, data, scatterplot, line, r, or estimate, etc.) that you found particularly important or interesting.
You may submit all of your project in one document or a combination of documents, which may consist of word processing documents or spreadsheets or scanned handwritten work, provided it is clearly labeled where each task can be found. Be sure to include your name. Projects are graded on the basis of completeness, correctness, ease in locating all of the checklist items, and strength of the narrative portions.

DATA COLLECTED
Researchers interested in determining if there is a relationship between death anxiety and religiosity conducted the following study. Subjects completed a death anxiety scale (high score = high anxiety) and also completed a checklist designed to measure an individuals degree of religiosity (belief in a particular religion, regular attendance at religious services, number of times per week they regularly pray, etc.) (high score = greater religiosity . A data sample is provided below (Death Anxiety and Religiosity)

38 4
42 3
29 11
31 5
28 9
15 6
24 14
17 9
19 10
11 15
8 19
19 17
3 10
14 14
6 18

(a) Use your equation to determine the “Religiosity” of a person that has a “Death Anxiety” score of 22.
(b) If someone had a “Religiosity” score of 25, what would you predict for their “Death Anxiety” score?

Project 2

Instructions
Pick a problem and post the number that you have chosen (so no one else picks that same problem). Use the data to create a graph of the data, then analyze the data to find the “best fit” equation for that data: linear, quadratic or exponential only (you can round your numbers in your equations to 4 decimal places). Then use that equation to answer any additional questions for your particular problem.

It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizes, etc.) would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students achievement test scores (she purposefully did not look at this data until after she submitted students grades) and the overall g.p.a. for each student computed over the entire year. The data for her class are provided below (Achievement and G.P.A.)

98 3.6
96 2.7
94 3.1
88 4.0
91 3.2
77 3.0
86 3.8
71 2.6
59 3.0
63 2.2
84 1.7
79 3.1
75 2.6
72 2.9
86 2.4
85 3.4
71 2.8
93 3.7
90 3.2
62 1.6

(a) If a student scored a 93 on the achievement test, what would be their predicted G.P.A.?
(b) If a student scored a 68 on the achievement test, what would be their predicted G.P.A.?

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Linear project: Achievement and G.P.A

It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizes, etc.) would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students achievement test scores (she purposefully did not look at this data until after she submitted students grades) and the overall g.p.a. for each student computed over the entire year....
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