A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Coefficients Standard Error Intercept 0.0136 x 1 0.7992 0.074
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.
A student used multiple
ANOVA
df SS
Regression 3 45.9634
Residual 11 2.6218
Coefficients Standard Error
Intercept 0.0136
x 1 0.7992 0.074
x2 0.2280 0.190
x3 -0.5796 0.920
Required:
c. Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance.
d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
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