Question

Here is the "theoretical" regression equation: y_i = β₀ + β₁x_i + ε_i 1. Select the appropriate name for each component of the equation.

y_i:  ---Select--- The linear correlation coefficient

The population intercept The estimated intercept

The population slope

The estimated slope The LOBF

The "random error" term

The predictor variable

The response variable

The confounding variable

The sampling bias

β₀:  ---Select--- The linear correlation coefficient

The population intercept

The estimated intercept

The population slope

The estimated slope The LOBF

The "random error" term

The predictor variable

The response variable

The confounding variable

The sampling bias

β₁:  ---Select---

The linear correlation coefficient

The population intercept

The estimated intercept

The population slope

The estimated slope The LOBF

The "random error" term

The predictor variable

The response variable

The confounding variable

The sampling bias

x_i:  ---Select---

The linear correlation coefficient

The population intercept

The estimated intercept

The population slope '

The estimated slope

The LOBF

The "random error" term

The predictor variable

The response variable

The confounding variable

The sampling bias

ε_i:  ---Select---

The linear correlation coefficient

The population intercept

The estimated intercept

The population slope

The estimated slope

The LOBF

The "random error" term

The predictor variable

The response variable

The confounding variable

The sampling bias

2. Select the appropriate interpretation for each term below.

R²:  ---Select--- The change in the predicted value of Y that is associated with a one unit increase in X

The estimated slope, divided by the standard error of the estimated slope

The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable

The difference between the observed and predicted values of the response

The magnitude of the variability in the residuals

The width of the interval for a new observation

A predicted value of the response variable

The predicted value of the response variable when the predictor variable equals zero

The standard amount by which the estimated value of the slope should differ from its population value

The probability of obtaining a test statistic at least as large as the one obtained, assuming the null hypothesis is true

β₀:  ---Select--- The change in the predicted value of Y that is associated with a one unit increase in X The estimated slope, divided by the standard error of the estimated slope The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable The difference between the observed and predicted values of the response The magnitude of the variability in the residuals The width of the interval for a new observation A predicted value of the response variable The predicted value of the response variable when the predictor variable equals zero The standard amount by which the estimated value of the slope should differ from its population value The probability of obtaining a test statistic at least as large as the one obtained, assuming the null hypothesis is true

β₁:  ---Select--- The change in the predicted value of Y that is associated with a one unit increase in X The estimated slope, divided by the standard error of the estimated slope The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable The difference between the observed and predicted values of the response The magnitude of the variability in the residuals The width of the interval for a new observation A predicted value of the response variable The predicted value of the response variable when the predictor variable equals zero The standard amount by which the estimated value of the slope should differ from its population value The probability of obtaining a test statistic at least as large as the one obtained, assuming the null hypothesis is true

se_(b1):  ---Select--- The change in the predicted value of Y that is associated with a one unit increase in X The estimated slope, divided by the standard error of the estimated slope The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable The difference between the observed and predicted values of the response The magnitude of the variability in the residuals The width of the interval for a new observation A predicted value of the response variable The predicted value of the response variable when the predictor variable equals zero The standard amount by which the estimated value of the slope should differ from its population value The probability of obtaining a test statistic at least as large as the one obtained, assuming the null hypothesis is true

"y-hat":  ---Select--- The change in the predicted value of Y that is associated with a one unit increase in X The estimated slope, divided by the standard error of the estimated slope The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable The difference between the observed and predicted values of the response The magnitude of the variability in the residuals The width of the interval for a new observation A predicted value of the response variable The predicted value of the response variable when the predictor variable equals zero The standard amount by which the estimated value of the slope should differ from its population value The probability of obtaining a test statistic at least as large as the one obtained, assuming the null hypothesis is true

Answer 1

#1) Regression equation: y_i = β₀ + β₁x_i + ε_i

Y_i is the response variable.

β₀:  The population intercept

β₁: The population slope

x_i:  The predictor variable

ε_i: The "random error" term

#2)Select the appropriate interpretation for each term below.

R²: The proportion of variability in the response variable that is "explained by" or "attributable to" variability in the predictor variable.

β₀: The predicted value of the response variable when the predictor variable equals zero.

β₁: The change in the predicted value of Y that is associated with a one unit increase in X.

se_(b1): The standard amount by which the estimated value of the slope should differ from its population value.

"y-hat": Predicted value of the response variable.