12. Regression

In linear regression using the least squares method, the least squares regression line minimizes the sum of the $e^2$, where $e$ represents the residuals (the differences between observed and predicted values).

In the linear regression equation $\mathrm{performance}=9.32+0.52\times \mathrm{aptitude score}$, what is the value of the slope?

In simple linear regression analysis, which of the following best describes the method of least squares?

In the context of linear regression using the least squares method, why is the graph shown considered a line of best fit?

In simple linear regression using the least squares method, which plot will produce a straight line if the model assumptions are satisfied?

Given a linear regression equation of the form $y=a+bx$ with $b=3$ and $a=-6$, what is the predicted value of $y$ when $x=4$?

In the context of linear regression using the least squares method, what does each point on the least-squares regression line represent?

Which of the following is NOT true about simple linear regression using the least squares method?

Given a set of data points, which of the following equations represents the least squares regression line ($LSRL$) for predicting $y$ from $x$?

In regression analysis, which method is commonly used to estimate the parameters of a linear model by minimizing the sum of the squared differences between observed and predicted values?$min\left(\sum _{i=1}^n{(y_i-{ŷ}_i)}^2\right)$

Which of the following is not one of the purposes of a line of regression in linear regression using the least squares method ($\text{least squares}$)?

In linear regression using the least squares method, which expression can be simplified to find the slope of the trend line in the scatterplot?

In linear regression using the least squares method, which of the following equations best approximates the line of best fit for a set of data points $(x,y)$?

Given the least squares regression equation $y=a+bx$, what does the coefficient $b$ represent?

In linear regression using the least squares method, the line of best fit for a scatterplot always passes through which pair of points?