The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _______
a. the variance
b. a residual
c. a prediction interval
d. the standard error
The least squares regression line is the unique line such that the sum of the squared vertical (y) distance between the data points and the line is the smallest possible.
The least squares regression line of y on x is the line that makes the sum of the squared residuals as small as possible.
The least regression line is,
Here, represents the dependent variable
represents the independent variable
represents the intercept variable
represents the slope variable.
The residual formula is,
The available statement is the difference between the observed value of the dependent and the value of the predicted by using the regression equation.
A residual is the vertical difference between each data point and the regression line.
The correct answer is: B
Residual
The difference between the observed value of the dependent and the value of the predicted by using the regression equation is residual
Ans:The correct answer is Residual.
The difference between the observed value of the dependent variable and the value predicted by using...
On a regression output, which gives the average size of deviation between observed y and predicted y? a. Multiple R-Squared b. F-Statistic c. Adjusted R-Square d. Residual standard error
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the _____. a. correlation coefficient b. coefficient of determination c. confidence interval estimate d. standard error of t
For a pair of sample x- and y-values, the _______ is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.
1. a. At any given combination of values , the assumptions for the multiple regression model require that the population of potential error term values has? b. What is the point estimate for the constant variance? c.Which of the following is the sum of the squared differences between the predicted values of the dependent variable and the mean of the dependent variable, the explained variation? d.The null hypothesis for the overall F-test states that: At least one ββis not equal...
The multiple correlation of several variables with a dependent variable is a) less than the largest individual correlation. b) equal to the correlation of the dependent variable to the values predicted by the regression equation. c) noticeably less than the correlation of the dependent variable to the values predicted by the regression equation. d) It could take on any value
The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = β0 + β1x1 + β2x2 + β3x3 +...+ βpxp is: a. a multiple regression equation. b. a simple linear regression model. c. a multiple nonlinear regression model. d. an estimated multiple regression equation.
Consider a multiple regression model of the dependent variable y on independent variables x1, x2, and x3: Using data with n = 12 observations for each of the variables, a researcher obtains the following estimated regression equation for the above model y0.5216 + 1.2419x1 + 0.3049x2 - 0.0217x3 The standard error of estimate for this equation is s0.6489 The table below gives the values for the independent and dependent variables and their corresponding predicted values, residuals, and leverage Predicted Value...
Select all of the following statements that are true about linear regression analysis of quantitative variables. If the purpose of our regression model is prediction, it does not matter which variables we define as the explanatory and response variable. The observed values of Y will fall on the estimated regression line, while the predicted values of Y will vary around the regression line. The purpose of linear regression is to investigate if there exists a linear relationship between a response...
The ______ is a measure of the error in using the estimated regression equation to predict the values of the dependent variable in a sample. A. sum of squares due to regression (SSR) B. sum of squares due to error (SSE) C. erorr term D. residual
2. Use the data in hpricel.wfl uploaded on Moodle for this exercise. We assume that all assump- tions of the Classical Linear Model are satisfied for the model used in this question. (a) Estimate the model and report the results in the usual form, including the standard error of the regression. Obtain the predicted price when we plug in lotsize - 10, 000, sqrft - 2,300, and bdrms- 4; round this price to the nearest dollar. (b) Run a regression...