The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Shown here are the CCIs for nine years and the median household incomes for the same nine years published by the U.S. Census Bureau. Determine the equation of the regression line to predict the CCI from the median household income. Does median household income appear to be a good predictor of the CCI? Why or why not?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Situation:
The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a
CCI Median Household Income ($1,000)
116.8 37.415
91.5 36.770
68.5 35.501
61.6 35.047
65.9 34.700
90.6 34.942
100.0 35.887
104.6 36.306
125.4 37.005
Action
Perform a
Scatter Diagram
PLACE THE ANSWER FOR PART a IN THIS SECTION DESCRIBING THE DATA TREND WITH RESPECT TO SIGN OF THE SLOPE AND THE INTERPRETATION OF THS SLOPE OF THE REGRESSION EQUATION.
- R, R2 and 1-R2
PLACE THE ANSWER FOR PART b IN THIS SECTION PROVIDING THE VALUES OF R, R2, AND 1-R2 AND INTERPRETATION OF EACH ONE OF THESE VALUES.
- Show the regression equation. Comment on the interpretation of the slope of regression equation.
PLACE THE ANSWER FOR PART c IN THIS SECTION DESCRIBING THE REGRESSION EQUATION WITH RESPECT TO HOW WELL IT FITS THE DATA CONSIDERING THE VALUES COMPUTED IN PART b OF THE PROBLEM.
- What is the standard error of estimate value? What is the interpretation of this value?
PLACE THE ANSWER FOR PART d IN THIS SECTION PROVIDING THE VALUE OF STANDARD ERROR OF ESTIMATE AND ITS INTERPRETATION.
- Conduct the appropriate test of hypothesis for the regression model. Use a .05 level of significance. Does median household income appear to be good predictor of the CCI? Why or why not?
PLACE THE ANSWER FOR PART e IN THIS SECTION. SHOW THE Ho AND Ha. SHOW THE COMPUTED p-VALUE. COMPARE p-VALUE TO SIGNIFICANCE LEVEL AND STATE WHETER Ho SHOULD BE REJECTED BASED ON THIS COMPARISON. BASED ON WHETHER Ho IS/IS NOT REJECTED, STATE WHETHER MEDIAN HOUSEHOLD INCOME APPEARS TO BE A GOOD PREDICTOR OF CCI.
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