Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?
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.
Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the following
regression results:
Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78.
(23.5) (16.4)
Another researcher is interested in the same regression, but makes an error
when entering the data into a regression program: The researcher enters
each observation twice, ending up with 100 observations (with observation
1 entered twice, observation 2 entered twice and so forth).
a. Using these 100 observations, what results will be produced by the
regression program? (Hint: Write the “incorrect” values of the sample
means, variances, and
values. Use these to determine the regression statistics.)
Ŷ = ____ + ____X, SER = ____, R2 = ____.
(____) (____)
b. Which (if any) of the internal validity conditions are violated?
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