a. Find the least squares estimate of the regression line with assuming the simple linear regression is valid. (Find the coefficients of the model)
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. Find the least squares estimate of the regression line with assuming the simple linear regression
is valid. (Find the coefficients of the model)
b. Write down the probabilistic and deterministic models (equations) with the estimated
coefficients.
c. Find the sum of squares of the regression and error and their corresponding mean squares.
d. Test the usefulness of the regression model and the slope of the line of means.
e. Find the
interpret your results.
f. Estimate the average value of the steel tensile strength when the carbon amount is 320 mg/g, and
construct a 95% confidence interval for this estimate.
g. Predict the strength of the steel when the carbon amount is 200 mg/g and construct a 95%
prediction interval.
h. Plot Residuals vs Fitted Value graph and comment on the regression model.
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