Q. No. 3. To the Board of Revenue , the deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions are as follows: a. Develop a scatter diagram with adjusted gross income as the independent variable. b. Determine the correlation coefficient. c. Determine the standard error of estimate d. Determine the coefficient of determination and interpret it. e. At the .05 significance level, is it reasonable to conclude that there is a positive relationship between the variables? What is the p-value? f. Develop the estimated regression equation. g. Estimate a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of $20,400, would the agent’s request for an audit appear justified?
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.
Q. No. 3.
To the Board of Revenue , the deductions depends on the taxpayer’s adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions are as follows:
a. Develop a
b. Determine the
c. Determine the standard error of estimate
d. Determine the coefficient of determination and interpret it.
e. At the .05 significance level, is it reasonable to conclude that there is a positive relationship between the variables? What is the p-value?
f. Develop the estimated regression equation.
g. Estimate a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of $20,400, would the agent’s request for an audit appear justified?
Step by step
Solved in 4 steps with 4 images
