ARTS 280 - Correlation And Linear Regression Assignment

Assignment Task

Question 1: Research Scenario (SPSS required)

Given the data provided, your task is to determine if watching television is associated with heightened cholesterol levels. The data is based on a random sample of 200 people and information was collected on the following two variables.

Television Hours: the number of hours a person spends watching television on a typical week
Cholesterol: cholesterol levels measured in mg/dL

1) Explore the data and state if linear regression is a reasonable option for analyzing the relationship between television hours and cholesterol levels. Copy and paste relevant SPSS figure(s) and provide a written explanation.

2) Write the population model Describe each of the terms in the equation.

3) State the null and alternative hypotheses.

4) Perform linear regression to examine if time spent watching television has an impact on cholesterol levels.

1. Copy/paste the following output tables: “Model Summary” (the table with R and R²) & “Coefficients table” (the table containing the regression coefficients).
2. Using the above tables, write the fitted model equation and provide an interpretation of the regression coefficient(s). After interpreting the regression coefficient(s), state whether your findings are statistically significant.
3. Provide an interpretation of r and R².
4. Provide a non-technical summary of your findings without using statistical jargon so that someone without a statistics background can understand 

Question 2: Research Scenario (SPSS required)

You are interested in determining if an association exists between social media usage, study hours, and exam performance. The data is based on a random group of 200 students from ENG 1001.  

Social Media: the number of hours a person spends on social media on an average week.

Study: the number of hours a person spends studying on an average day Exam Performance: percentage score on exam (0 ~ 100)

Your task is to see if social media use and the amount of study hours has an impact on final exam performance for a random sample of 200 engineering students.

1. Explore the data. Copy and paste any relevant SPSS figure(s) and state if linear regression is a reasonable method for analyzing the data.
2. Write out the population model for multivariable regression. Describe each of the terms in the equation.
3. State the null and alternative hypotheses. 
4. Perform a multiple regression analysis to determine if the amount of social media use and the number of study hours has an impact on final exam performance.
    
   • Copy/paste the following output tables: Model Summary, & Coefficients.
   • Using the Coefficients table, write the fitted model equation and provide an interpretation of the regression coefficients. After interpreting the regression coefficient(s), state whether your findings are statistically significant. 
   • Provide an interpretation of r and R².
   • Provide a real-world summary of your findings without using statistical jargon.

Question 3: Research Scenario (SPSS not required)

Suppose you are interested in examining the relationship between annual income and age. Age has been operationalized as a binary variable – Younger adults are those between 18 ~ 40; older adults are people who are 41+)

Age Bracket: binary variable, (0 = Younger Adults, 1 = Older Adults)

Income: annual income

In particular, you want to determine if younger adults make more or less income than their older counterparts. The following linear model was proposed to analyse the data.

Shown below is the output from the regression analysis.  

1) Using the above table, write the fitted model equation and provide an interpretation of the regression coefficient(s). After interpreting the regression coefficient(s), state whether your findings are statistically significant.

2) Provide a non-technical summary of your findings without statistical jargon.

Question 4: Research Scenario (SPSS not required)

You are curious about the relationship between cholesterol levels, smoking status, and age.

Smoking Status: (0 = non-smoking, 1 = smoking)

Age: a person’s age in years (rounded to the floor value)

Cholesterol: cholesterol levels measured in mg/dL

To investigate if smoking and age are linearly associated with cholesterol levels, the following model constructed:

Shown below is output from the regression analysis and data visual.  

1) The regression coefficient, , corresponds to what predictor variable(s)?

2) Look closely at the regression coefficients. Would you choose to interpret all of them in this model (yes, or no?). Briefly explain why.

3) Using the above table, write the fitted model equation. 

4) What were the findings of this analysis? Describe.
(Hint: does your interpretation of the findings

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