Purchase Solution

Correlation and regression: key informaiton

Not what you're looking for?

Ask Custom Question

Use the data in the table, which shows the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years. (Source: U.S. Commerce Department, Bureau of Economic Analysis)

Personal income, x Personal outlays, y
5.6 4.6
5.8 4.9
6.2 5.2
6.5 5.5
6.9 5.8
7.4 6.1
7.8 6.5
8.4 7.0
8.7 7.3
8.9 7.7
9.2 8.0

1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.

2. Calculate the correlation coefficient r. What can you conclude?

3. Test the level of significance of the correlation coefficient r. Use a = 0.05.

4. Find the equation of the regression line for the data. Include the regression line in the scatter plot.

5. Use the regression line to predict the personal outlays when the personal income is 5.3 trillion dollars.

6. Find the coefficient of determination and interpret the results.

7. Find the standard error of estimate and interpret the results.

8. Construct a 95% prediction interval for personal outlays when personal income is 6.4 trillion dollars. Interpret the results.

Purchase this Solution
Solution Summary

A correlation and regression analysis has been carried out. A scatter plot for the data has been constructed. The correlation coefficient has been calculated and tested for significance. Equation of the regression line for the data has been calculated. The regression line has been used to make prediction. The coefficient of determination and the standard error of estimate have been calculated.

Solution Preview

Please see attached file:
For Exercises 1-8, use the data in the table, which shows the personal income and outlays (both in trillions of dollars) for Americans for 11 recent years. (Source: U.S. Commerce Department, Bureau of Economic Analysis)

Personal income, x   Personal outlays, y
5.6 4.6 0.995917753
5.8 4.9
6.2 5.2
6.5 5.5
6.9 5.8
7.4 6.1
7.8 6.5
8.4 7.0
8.7 7.3
8.9 7.7
9.2 8.0

1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.

The data appear to have a positive linear correlation as with an increase in personal income, personal outlays is increasing.

2. Calculate the correlation coefficient r.  What can you conclude?

(X) ...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

View More Free Quizzes
Related BrainMass Solutions

  • Correlation and Simple Linear Regression Using SPSS

    546510 Correlation and Simple Linear Regression Using SPSS 1. Use SPSS to provide key descriptive statistics for each continuous and ordinal variable (mean, median, standard deviation) in a table format.

  • Regression : key information

    192086 Regression : key information 1. List one unclear concept regarding regression and provide an example from your personal or work life where regression could be used to show a relationship between two variables. 2.

  • Statistics: Correlation coefficient, regression analysis

    For correlation see excel sheet "correlation". The correlation coefficient is -0.8301. It indicates that number of times wash hands and number of colds are negatively correlation.

  • Test whether age is a variable between education and hours worked

    Restate the RQ; provide descriptive analysis (not needed unless you consider there is a key point here); ANOVA (fit); correlation analysis (could variables co-vary excessively); R-Square; coefficients - the key is to answer the question: is age a spurious

  • Simple Harmonic Motion: Key Informaiton

    97350 Simple Harmonic Motion: Key Informaiton A hole is drilled straight through the center of the earth and a particle is dropped into the hole.

  • Regression Analysis

    Regression Analysis can predict the outcome of a given key business indicator (dependent variable) based on the interactions of other related business drivers (explanatory variables).

  • Regression Analysis: AIU benefits data. Construct charts

    Please refer to excel document: data set and data key (attached) and word document: regression analysis instructor comments (attached) to do the assignment. The solution file is attached.

  • What is Relational Database and Primary Key in Database?

    You need such a database to store and model real world informaiton such as banking, inventory, mailing list, etc. Each table contains rows and columns. Rows represent data tuples and refers to, possibly, different instances or examples of data.

  • Question on use of regression output in business

    The key statistics reported in a regression output, which are critical for business uses are: R - Coefficient of Correlation: The correlation between the predicted and the actual value of dependent variable R square - Coefficient of Determination

View More Related Solutions