Question

What statistic is used to estimate

a. The $y-$intercept of the population regression line?

b. The slope of the population regression line?

c. The common conditional standard deviation, $\sigma$, of the response variable?

Short answer

(a) ${\beta }_0$is the $y-$intercept of line $y={\beta }_0+6{\beta }_1$

(b) ${\beta }_1$is the slope

(c) The standard error of the estimate is the statistic used to produce a point estimate for the common conditional standard deviation $\sigma$.

Step-by-step solution

Part (a) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

Part (a) Step 2: Explanation

The $y-$intercept of the population regression line

${\beta }_0$Is the $y-$intercept of the population regression line$y={\beta }_0+6{\beta }_1.$

Part (b) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

Part (b) Step 2: Explanation

${\beta }_1$ is the slope of regression line$y={\beta }_0+x{\beta }_1$.

Part (c) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

Part (c) Step 2: Explanation

The standard error of the estimate is the statistic used to produce a point estimate for the common conditional standard deviation $\sigma$.

$S_e=\sqrt{\frac{SSE}{n-2}}$.