Answer true or false to each of the following statements and explain your answers.a. Correlations among values of the response variable have no effect whatsoever on statistical inferences based upon the t-statistics and F-statistic used in multiple linear regression.b. When there are errors in the measurements of the predictor variables, statistical inferences in regression analysis become less reliable.c. A nonrepresentative sample of the population of interest will have no effect on the regression model that is obtained.
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.
Answer true or false to each of the following statements and explain your answers.
a.
b. When there are errors in the measurements of the predictor variables, statistical inferences in
c. A nonrepresentative sample of the population of interest will have no effect on the regression model that is obtained.
a).
Correlation among values of the response variable underestimates the common conditional standard deviation. This produces larger values of t-statistics for testing utilities of predictors or F-statistics for utility of the regression, leading to rejection of the null hypothesis when it is true or more often.
Thus, the statement is False.
b).
The presence of measurement errors increases the variation in the data unnecessarily. The inferences drawn by analyzing a data with excessive error are unreliable.
Therefore, the statement is True.
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