A least squares regression line O always implies a cause and effect relationship between x and y can only be determined if a perfect linear relationship exists between x a O can be used to predict a value of y given a corresponding value of x none of these are correct
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- Above, a table was created to calculate the coefficients of the linear regression y=ax+b model for a data set using the least squares method. What is the coefficient a in this model?A least squares regression line ______. a. implies a cause-effect relationship between x and y b. may be used to predict a value of y if the corresponding x value is given c. can only be determined if a good linear relationship exists between x and y d. All of these answers are correct.For a least squares regression line, the sum of the residuals is __________. always negative sometimes positive and sometimes negative always zero always positive
- Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply.The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is NOT true in the multiple linear regression outputs? In the F-test ANOVA result, if Ho is rejected, this means that the regression model overall predicts the dependent variable significantly well. If a predictor is having a significant impact on our ability to predict the outcome then the regression coefficient b should be significantly different from 1.0. The F-test ANOVA assesses all of the regression coefficients jointly whereas the t-test for each coefficient examines them individually. It is possible that a model is significant, but not enough to conclude that any individual variable is significant.
- Define Least Squares Regression Unbiased Estimators α^, β^, σ^²?A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
- Suppose that a regression relationship is given by the following:Y = β0 + β1X1 + β2X2 + εIf the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation between X1 and X2 is 0, this will not be so. In fact, in that case the same estimate results whether or not X2 is included in the regression equation.a. Explain verbally why this statement is true.b. Show algebraically that this statement is true.Find the least square regression line.Explain with proof Least Squares Regression Unbiased Estimators y^
