Use the following linear regression equation to answer the questions. x1 = 1.7 + 3.9x2 – 8.5x3 + 2.2x4 Which variables are the explanatory variables? (Select all that apply.) x2x4x1x3 (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. constant ? x2 coefficient ? x3 coefficient ? x4 coefficient ?
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.
Use the following linear regression equation to answer the questions.
| constant | ? |
| x2 coefficient | ? |
| x3 coefficient | ? |
| x4 coefficient | ? |
(c) If x2 = 6, x3 = 7, and x4 = 4, what is the predicted value for x1? (Use 1 decimal place.)
Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?
Suppose x2 increased by 2 units. What would be the expected change in x1?
Suppose x2 decreased by 4 units. What would be the expected change in x1?
(e) Suppose that n = 18 data points were used to construct the given regression equation and that the standard error for the coefficient of x2 is 0.454. Construct a 99% confidence interval for the coefficient of x2. (Use 2 decimal places.)
| lower limit | ? |
| upper limit | ? |
(f) Using the information of part (e) and level of significance 10%, test the claim that the coefficient of x2 is different from zero. (Use 2 decimal places.)
| t | ? |
| t critical ± | ? |
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