Use the following linear regression equation to answer the questions. x3 = −15.4 + 4.0x1 + 8.2x4 − 1.2x7 (d)Suppose x1 and x7 were held at fixed but arbitrary values.If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be?If x4 increased by 3 units, what would be the corresponding expected change in x3?If x4 decreased by 2 units, what would we expect for the corresponding change in x3?(e) Suppose that n = 14 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.917. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.) lower limit upper limit (f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x4 is different from zero. (Round your answers to two decimal places.) t = t critical = ±
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.
If x4 increased by 1 unit, what would we expect the corresponding change in x3 to be?
If x4 increased by 3 units, what would be the corresponding expected change in x3?
If x4 decreased by 2 units, what would we expect for the corresponding change in x3?
(e) Suppose that n = 14 data points were used to construct the given regression equation and that the standard error for the coefficient of x4 is 0.917. Construct a 90% confidence interval for the coefficient of x4. (Round your answers to two decimal places.)
| lower limit | |
| upper limit |
(f) Using the information of part (e) and level of significance 5%, test the claim that the coefficient of x4 is different from zero. (Round your answers to two decimal places.)
| t | = | |
| t critical | = ± |
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