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1)

I don't understand the difference between β

For example, when we see a scattered plot with a least-square line of best fit, say, y = 8 + 5x, then βo=8, β1=5, right? What are the b

2)

Now I don't understand the difference between random error (ε

Thanks for explaining!

**"Simple linear regression model: Y**

We want to estimate β_{i}= β_{0}+ β_{1}X_{i}+ ε_{i}, i=1,...,n where n is the number of data points, ε_{i}is random errorWe want to estimate β

_{0}and β_{1}based on our observed data. The estimates of β_{0}and β_{1}are denoted by b_{0}and b_{1}, respectively."I don't understand the difference between β

_{0},β_{1}and b_{0},b_{1}.For example, when we see a scattered plot with a least-square line of best fit, say, y = 8 + 5x, then βo=8, β1=5, right? What are the b

_{0}and b_{1}all about? Why do we need to introduce b_{0},b_{1}?2)

**"Simple linear regression model: Y**

Fitted value of Y

Residual = vertical deviations = Y

where Y_{i}= β_{0}+ β_{1}X_{i}+ ε_{i}, i=1,...,n where n is the number of data points, ε_{i}is random errorFitted value of Y

_{i}for each X_{i}is: Y_{i}hat = b_{0}+ b_{1}X_{i}Residual = vertical deviations = Y

_{i}- Y_{i}hat = e_{i}where Y

_{i}is the actual observed value of Y, and Y_{i}hat is the value of Y predicted by the model"Now I don't understand the difference between random error (ε

_{i}) and residual (e_{i}). What is the meaning of ε_{i}? How are ε_{i}and e_{i}different?Thanks for explaining!

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