priscillianaw1

2022-10-08

Given a set of data with $11$ observations of two variables (response and predictor), I've been asked to "calculate the fitted values ${\hat{y}}_{i}=\hat{\alpha}+\hat{\beta}{x}_{i}^{\prime}$ and residuals ${e}_{i}={y}_{i}-{\hat{y}}_{i}$ by hand".

What is the question asking me to do here? I have thus far estimated the regression line for the data in the form ${\hat{y}}_{i}=\hat{\alpha}+\hat{\beta}{x}_{i}^{\prime}$ by calculating the coefficients $\alpha \text{}\mathrm{}\text{}\beta ,,\; but\; this\; doesn\text{'}t\; answer\; the\; original\; question\; alone.\; Where\; do\; I\; go\; from\; here?$

What is the question asking me to do here? I have thus far estimated the regression line for the data in the form ${\hat{y}}_{i}=\hat{\alpha}+\hat{\beta}{x}_{i}^{\prime}$ by calculating the coefficients $\alpha \text{}\mathrm{}\text{}\beta ,,\; but\; this\; doesn\text{'}t\; answer\; the\; original\; question\; alone.\; Where\; do\; I\; go\; from\; here?$

Piper Pruitt

Beginner2022-10-09Added 9 answers

If you have calculated $\hat{\alpha}$ and $\hat{\beta}$ you can compute the $11$ values of $\hat{{y}_{i}}$ by plugging in the $11$ values of ${x}_{i}$.

Compare the value predicted by the regression, $\hat{{y}_{i}}$, and the actual value it should be ${y}_{i}$.

Their difference is the residual.

Compare the value predicted by the regression, $\hat{{y}_{i}}$, and the actual value it should be ${y}_{i}$.

Their difference is the residual.

Read carefully and choose only one option

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