Project #74931 - Linear regression

 

Select 2 quantitative variables that you believe may be related in a specific population. After collecting your data, you will investigate the relationship by constructing a scatter plot, computing correlation, and conducting a linear regression analysis. 

 

 

Here are some example variables and corresponding research questions and hypotheses:


 

Batting averages and salaries among professional baseball players

  •   Population: Professional baseball players

  •   Explanatory Variable: Batting average

  •   ResponseVariable:Annualsalary

  •   Research Question: Is there a correlation between professional baseball players’ batting averages and their salaries?

  •   Hypothesis: Players with higher batting averages have higher salaries [positive correlation is hypothesized].

  • Calories and fat content in grocery store snack foods

  •   Population:Grocerystoresnackfoods

  •   Explanatory Variable: Fat content in grams per serving

  •   Response Variable: Calories per serving

  •   Research Question: Is there a correlation between snack food calories and fat content?

  •   Hypothesis: Snack foods with higher fat content also have higher calories [positive

    correlation is hypothesized]. 

 

 

ï‚· Engine horsepower and gas mileage in automobiles

  •   Population:Automobiles

  •   ExplanatoryVariable:Enginehorsepower(HP)

  •   Response Variable: Gas mileage (miles per gallon)

  •   Research Question: Is there a correlation between cars’ horsepower and their gas

    mileage?

  •   Hypothesis: Cars with higher horsepower have lower gas mileage [negative correlation

    is hypothesized]. 

 

 

Choose a research question that can be addressed using linear regression

Devise a plan to collect your data
Send an email to your instructor and obtain approval
Once your research question and data collection plan are approved, carry out your a. research:

  1. Collect data

  2. Conduct linear regression analysis, referring to guidelines below

  3. Write your results in a report, using the outline given below

 

Below is a detailed outline of the content that should be included in your report. Your report is expected to be a formal paper (not an outline). Your results should be stated in complete sentences, and your paper should be written in paragraph form. Although you may choose to use headings, you should not number your paragraphs.

  1. Introduction: State the topic of your study as a research question and/or as a specific hypothesis that you tested. Your hypothesis should indicate what type of correlation you expected to see (positive or negative) and how strong you expected the correlation to be (weak, moderate, or strong). Your hypothesis should describe a specific result that you expected to find AND the practical reason that you expected this result (your rationale).

  2. Define Population(s): Define clearly the population(s) that you intend for your study to represent. (Examples: all NFL football players, all cars manufactured this year, all biology majors at your school, all small towns in the Southeastern U.S., all PetSmart shoppers in your city, etc.)

 

  1. Define Variable(s): Define clearly the variable(s) that you obtained during your data collection (e.g., age, salary, price, miles per gallon, miles commuted one-way to school daily, etc.) This must be specific: “time spent watching TV” is too vague; “number of hours spent watching TV in the last 3 days” would be specific enough. If your variable is a measurement (e.g., height) give units (e.g., inches).

  2. Data Collection: Describe your data collection process and sampling strategy. If you located data on a website, provide the URL and tell how you selected individuals from that website to include in your sample. If you obtained data from an agency, office, store,or other similar source, explain where you went and how you selected individuals to include in your sample. If you surveyed individuals directly or took measurements, describe how you selected individuals for the sample. If you used a survey, this section must include a copy of your survey. No matter what data collection process you used, address: a) what steps you took to avoid bias in your sample; and b) whether you believe the sample(s) you obtained were representative of the population. Tell why or why not. You must include a table with all of your raw (not summarized) data as an appendix at the end of the report.

  3. Study Design. Identify the statistical procedures you used to analyze your data. Give relevant design details (e.g., which variable was selected as the explanatory variable, and which the response variable? Why? What type of correlation did you expect? And so on.)

  4. Results: Descriptive Statistics. Give descriptive statistics for each of your two quantitative variables. Note that you will be reporting summary statistics for both your explanatory variable and your response variable. Report each set of descriptive statistics using both a table and a chart as described below. All tables and charts should be placed directly in your report.

    a) Table: Give sample size, mean, standard deviation, and 5-number summary.

    b) Chart: Show a histogram that illustrates the distribution of the variable.

  5. Results: Statistical Analysis. Report the results of your analysis; include items below.

    1. a)  Scatter plot with a graph of the regression line

    2. b)  Value of the correlation coefficient r and interpretation of its meaning

    3. c)  Equation of the regression line

    4. d)  An example of a prediction using the regression equation

    5. e)  Discussion of the slope of the regression line and its meaning

    6. f)  Value of R2 for the regression model and interpretation of its meaning

  6. Findings: Interpret the results of your statistical analysis in the context of your original research question. Do your analyses support your expected findings? Explain. 

9.  Discussion: What conclusions, if any, do you believe you can draw as a result of your study? If the results were not what you expected, what factors might explain your results? What did you learn from the project about the population(s) you studied? What did you learn about the research variables? What did you learn about the specific statistical analysis you conducted? 

 

 

Identify variables & research question

Complete plan and obtain approval  due by Tuesday, 6/30

Subject Mathematics
Due By (Pacific Time) 07/15/2015 12:00 am
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