Term
What does linear regression refer to?
What's the goal of regression analysis? |
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Definition
representing relationships with linear equations where there is one dependent variable being explained by one or more independent variables.
Goal of regression analysis is to measure how changes in one variable, called a dependent or explained variable, can be explained by changes in one of more other variables called the independent or explanatory variables. |
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Term
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Definition
| Ordinary least squares (OLS) estimation is a process that estimtes the population parameters Bi with corresponding values for bi that minimise the squared residuals (i.e. error terms) |
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Term
| Write down the term that OLS seeks to minimise: |
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Definition
OLS seeks to minimise the sum of ei2, i.e. minimise:
[Yi - (b0 + b1 x Xi)]2 |
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Term
| In OLS the beta term for the slope b1 can be measured by (formula): |
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Definition
b1 = Cov(X,Y) / Var(X)
b1 = SumXiYi - (n * sample mean X * sample mean Y)
/
SumXi2 - (n * (sample mean X)2)) |
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Term
| What is RSS and how is it calculated? |
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Definition
RSS is the sum of squares that result from placing a given intercept and slope coefficient into the equationa dn computing the residuals, squaring the residuals and summing them.
It indicates how well the sample regression function explains the data. |
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Term
| With a population regression function what are the parameters called? Describe them... |
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Definition
A population regression function consists of parameters called regression coefficients.
The regression function will include an intercept term (expected value of Y when X is 0) and one slope coefficient (expected change in Y for unit change in X) |
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Term
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Definition
εi = Yi - E(Yi | Xi)
εi is the random component. It represents effects from independent variables not included in the model. |
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Term
| Describe the sample regression function: |
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Definition
an equation that represents a relationship between the X and Y variables tha tis based on the information in a sample of the population.
Contains a residual: ei = Yi - (b0 + b1 * Xi)
generally, as teh population and sample coefficients are almost always different, the residual will be different from the corresponding population error term, i.e.
ei ≠ εi |
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Term
| What does a linear regression model assume? |
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Definition
| a linear regression model assumes that the equation is linear in the variables and in the parameters |
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Term
| What does two-variable regression refer to? |
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Definition
regression that includes only one independent variable.
Multivariable regression includes two or more independent variables. |
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Term
| In OLS, whats the formula for b0 (the intercept coefficient) |
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Definition
| b0 = mean sample Y - (b1 * mean sample X) |
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