An analyst believes that the only important determinant of banks’ returns on assets (Y) is the ratio of loans to deposits (X). For a random sample of 20 banks, the sample regression line y = 0.97 + 0.47x was obtained with coefficient of determination 0.720. a. Find the sample correlation between returns on assets and the ratio of loans to deposits. b. Test against a two-sided alternative at the 5% significance level the null hypothesis of no linear association between the returns and the ratio.
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.
An analyst believes that the only important determinant of banks’ returns on assets (Y) is the ratio of loans to deposits (X). For a random sample of 20 banks, the sample regression line
y = 0.97 + 0.47x
was obtained with coefficient of determination 0.720.
a. Find the sample
b. Test against a two-sided alternative at the 5% significance level the null hypothesis of no linear association between the returns and the ratio.
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