Applying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.ExercisesApplying the Concepts and SkillsIn each of Exercises,a. find the regression equation for the data points.b. graph the regression equation and the data points.c. describe the apparent relationship between the two variables under consideration.d. interpret the slope of the regression line.e. identify the predictor and response variables.f. identify outliers and potential influential observations.g. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.Tax Efficiency.Tax efficiency is a measure, ranging from 0 to 100, of how much tax due to capital gains stock or mutual funds investors pay on their investments each year; the higher the tax efficiency, the lower is the tax. In the article “At the Mercy of the Manager” (Financial Planning, Vol. 30(5), pp. 54–56), C. Israelsen examined the relationship between investments in mutual fund portfolios and their associated tax efficiencies. The following table shows percentage of investments in energy securities (x) and tax efficiency ( y) for 10 mutual fund portfolios. For part (g), predict the tax efficiency of a mutual fund portfolio with 5.0% of its investments in energy securities and one with 7.4% of its investments in energy securities. x 3.1 3.2 3.7 4.3 4.0 5.5 6.7 7.4 7.4 10.6 y 98.1 94.7 92.0 89.8 87.5 85.0 82.0 77.8 72.1 53.5
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.
Applying the Concepts and Skills
In Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.
Exercises
Applying the Concepts and Skills
In each of Exercises,
a. find the regression equation for the data points.
b. graph the regression equation and the data points.
c. describe the apparent relationship between the two variables under consideration.
d. interpret the slope of the regression line.
e. identify the predictor and response variables.
f. identify outliers and potential influential observations.
g. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.
Tax Efficiency.Tax efficiency is a measure,
| x | 3.1 | 3.2 | 3.7 | 4.3 | 4.0 | 5.5 | 6.7 | 7.4 | 7.4 | 10.6 |
| y | 98.1 | 94.7 | 92.0 | 89.8 | 87.5 | 85.0 | 82.0 | 77.8 | 72.1 | 53.5 |
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