Based on a sample of 25 observations, the population regression modelyi = β0 + β1x1 + εiwas estimated. The least squares estimates obtained were as follows:b0 = 15.6 and b1 = 1.3The total and error sums of squares were as follows:SST = 268 and SSE = 204a. Find and interpret the coefficient of determination.b. Test, against a two-sided alternative at the 5% significance level, the null hypothesis that the slope of the population regression line is 0.c. Find a 95% confidence interval for β1.
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.
Based on a sample of 25 observations, the population regression model
yi = β0 + β1x1 + εi
was estimated. The least squares estimates obtained were as follows:
b0 = 15.6 and b1 = 1.3
The total and error sums of squares were as follows:
SST = 268 and SSE = 204
a. Find and interpret the coefficient of determination.
b. Test, against a two-sided alternative at the 5% significance level, the null hypothesis that the slope of the population regression line is 0.
c. Find a 95% confidence interval for β1.
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