Data are given below on the adjusted gross income x and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation = 5.16 + .14x, the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $57.5 thousand is $13,210. Adjusted Gross Income ($1000s) 22, 27, 32, 48, 65, 85, 120 Reasonable Amount of Itemized Deductions ($1000s) 9.6, 9.6,10.1, 11.1, 11.5, 17.7, 23.5 Develop a 95% confidence interval for the mean amount of total itemized deductions (in thousands of dollars) for all taxpayers with an adjusted gross income of $57,500. (Round your answers to two decimal places. $ ( , )
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.
Data are given below on the adjusted gross income x and the amount of itemized deductions taken by taxpayers. Data were reported in thousands of dollars. With the estimated regression equation = 5.16 + .14x, the point estimate of a reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $57.5 thousand is $13,210.
Adjusted Gross Income ($1000s)
22, 27, 32, 48, 65, 85, 120
Reasonable Amount of Itemized Deductions ($1000s)
9.6, 9.6,10.1, 11.1, 11.5, 17.7, 23.5
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Develop a 95% confidence interval for the mean amount of total itemized deductions (in thousands of dollars) for all taxpayers with an adjusted gross income of $57,500. (Round your answers to two decimal places.$ ( , )
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Develop a 95% prediction$ ( , )
interval estimate for the amount of total itemized deductions (in thousands of dollars) for a particular taxpayer with an adjusted gross income of $57,500. (Round your answers to two decimal places.) -
Use your answer to part (b) to give the IRS agent a guideline as to the amount of total itemized deductions (in thousands of dollars) a taxpayer with an adjusted gross income of $57,500 could claim before an audit is recommended. (Round your answer to two decimal places.)
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