Is LSRL resistant?

Is LSRL resistant?

Is the least squares regression line resistant? Neither r nor least-squares regression lines are resistant to outliers. Outliers greatly affect both.

Is coefficient of determination resistant?

The correlation coefficient and the LSRL are both non-resistant measures. Correlation coefficient: There is a direction, strength, type of association between x and y. If no pattern exists between the points in the residual plot, then the association is linear.

Is the LSRL the line of best fit?

The LSRL fits “best” because it reduces the residuals. The Least Squares Regression Line is the line that minimizes the sum of the residuals squared. In other words, for any other line other than the LSRL, the sum of the residuals squared will be greater. This is what makes the LSRL the sole best-fitting line.

Does the least-squares regression line pass through the mean?

This middle point has an x coordinate that is the mean of the x values and a y coordinate that is the mean of the y values. The least-squares regression line always passes through the point (x, y). This means that, regardless of the value of the slope, when X is at its mean, so is Y.

What percentage of variation in Y is explained by the least squares model?

The least squares regression line is a horizontal line through the mean of Y. The proportion of Y variability accounted for by the linear relationship = r2 = 0. The proportion of Y variability left unexplained = 1, or 100%. Figure 2.

Is the LSRL resistant to outliers?

The y-intercept and slope of the LSRL will change, but the value of r will be the same for both scatter plots. Is correlation r a resistant measure? No. Outliers greatly affect the value of r, therefore, correlation r is not a resistant measure.

Is R2 equal to correlation?

The correlation, denoted by r, measures the amount of linear association between two variables. The R-squared value, denoted by R 2, is the square of the correlation. It measures the proportion of variation in the dependent variable that can be attributed to the independent variable.

What does an R2 value of 0.9 mean?

What does an R-Squared value of 0.9 mean? Essentially, an R-Squared value of 0.9 would indicate that 90% of the variance of the dependent variable being studied is explained by the variance of the independent variable.

What is the least squares line of best fit?

The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve. Least squares regression is used to predict the behavior of dependent variables.

What does R 2 tell you?

R-squared (R2) is a statistical measure that represents the proportion of the variance for a dependent variable that’s explained by an independent variable or variables in a regression model.

What is the standard deviation of the lsrl?

DESCRIPTIVE STATISTICS- •The mean for non-exercise activity is about 325 calories with a standard deviation of about 258 calories with a spread (based on range) of 794 calories. •The mean for fat gain is 2.39 kilograms with a standard deviation of 1.14 kilograms and a spread (based on range) of 3.8 calories. Equation of LSRL

What is the name of the least squares regression line?

The name of the least squares line explains what it does. We start with a collection of points with coordinates given by (xi, yi). Any straight line will pass among these points and will either go above or below each of these.

What is the y intercept of the lsrl equation?

The Y intercept a = 3.505kg is the fat gain estimated by this model if NEA does not change when a person overeats. LSRL EQUATION: Y hat = 3.51- .0034X (better to use words) (Fat Gain) hat = 3.51- .0034(NEA) Graph the LSRL on our Scatterplot LSRL EQUATION: Y hat = 3.51- .0034X (Fat Gain) hat = 3.51- .0034(NEA) Not covered TODAY…