There are four conditions that should be at least approximately true for linear regression. A plot...
There are four conditions that should be at least approximately true for linear regression. A plot of residuals versus the x values can be used to check which of the following conditions:
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A straight line is the best model to describe the association between x and y, AND the variance of the values of y at each value of x should be the same. |
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Observations in the sample are independent of each other AND there should be no extreme outliers |
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The distribution of the values of y at each value of x should be normal AND there should be no extreme outliers |
Homework Answers
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There are four conditions that should be at least approximately
true for linear regression. A plot...
QUESTION 19 For the following software output, check each assumption/condition to run linear regression and state...
QUESTION 19 For the following software output, check each assumption/condition to run linear regression and state whether it is appropriate to use linear regression. Bivariate Fit of pluto By alpha 20 15 10 5 0 e 0.05 0.15 C 0.1 alpha Linear Fit Linear Fit pluto -0.597417 16543195*alpha Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.915999 0.911999 2.172963 6.73913 23 Analysis of Variance Sum of DF Squares Mean Square Source...
Which of the following is a diagnostic plot for regression? O A. Scatterplot of y versus...
Which of the following is a diagnostic plot for regression? O A. Scatterplot of y versus x to check linearity O B. Scatterplot of residuals versus predicteds to check for constant variance or nonlinearity ° C. Histogram of residuals to check for normality O D. All of the above are diagnostic plots for regression
Which of the following are assumptions for the linear regression model? CHECK THAT ALL MAY APPLY!!! Select one or more: a. Regression function (i.e., equation) is linear. b. Error terms are normall...
Which of the following are assumptions for the linear regression model? CHECK THAT ALL MAY APPLY!!! Select one or more: a. Regression function (i.e., equation) is linear. b. Error terms are normally distributed. c. Error terms are independent. d. Error terms have constant variance. e. Regression model fits all observations (i.e., no outliers).
Decide (with short explanations) whether the following statements are true or false. e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary s...
Decide (with short explanations) whether the following
statements are true or false.
e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
Group Assignment #8-Linear regression review You have the following sample data for y (dependent ...
Needs to be done in Matlab
Group Assignment #8-Linear regression review You have the following sample data for y (dependent variable) versus x (independent variable) x [1.1 2.0 3.1 3.9 5.1 6.0 7.3 7.8 9.1 10.4] y [0.8 2.1 2.9 4.3 4.9 5.9 7.0 8.3 8.7 9.9] a. Solve for the regression line and report a and b. b. Plot the regression line overlaid with the sample data points c. Solve for the error term (residuals) and plot residuals vs....
What do we mean by “regression toward the mean?” A. The linear regression equation can be...
What do we mean by “regression toward the mean?” A. The linear regression equation can be used to identify the average value of each variable in the model. B. Linear regression normalizes the scale of the variables so they have a mean of zero and standard deviation of 1. C. The phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on a second measurement. D. Outliers in the model...
Select all of the following statements that are true about linear regression analysis of quantitative variables....
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...
Below are given (a) A scatterplot of Y versus X and (b) A plot of residuals...
Below are given (a) A scatterplot of Y versus X and (b) A plot
of residuals versus fitted values after a simple linear regression
model was fit to the data. What is the equation of the fitted line?
Discuss what is indicated about the relationship between Y and X as
it relates to simple linear regression.
Fitted Line Plot Y = - 14.64 + 7.431 X R-Sq R-Sq (adj) 2.43700 91.9% 91.8% 1 > 20- 3 4 5 6 7...
Question 2: Suppose that we wish to fit a regression model for which the true regression...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
Since residuals measure how far the observations are from the regression line, they are often used...
Since residuals measure how far the observations are from the regression line, they are often used to assess the fit of the regression line to the data. We might display these vertical deviations graphically using a residual plot. By plotting the residuals against the explanatory variable x, we effectively magnify the deviations (that is, change the y-axis from response to vertical deviations), which allows for a better and closer examination of the deviations. Describe what a residual plot would look...
QUESTION 19 For the following software output, check each assumption/condition to run linear regression and state whether it is appropriate to use linear regression. Bivariate Fit of pluto By alpha 20 15 10 5 0 e 0.05 0.15 C 0.1 alpha Linear Fit Linear Fit pluto -0.597417 16543195*alpha Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.915999 0.911999 2.172963 6.73913 23 Analysis of Variance Sum of DF Squares Mean Square Source...
Which of the following is a diagnostic plot for regression? O A. Scatterplot of y versus x to check linearity O B. Scatterplot of residuals versus predicteds to check for constant variance or nonlinearity ° C. Histogram of residuals to check for normality O D. All of the above are diagnostic plots for regression
Decide (with short explanations) whether the following
statements are true or false.
e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
Needs to be done in Matlab
Group Assignment #8-Linear regression review You have the following sample data for y (dependent variable) versus x (independent variable) x [1.1 2.0 3.1 3.9 5.1 6.0 7.3 7.8 9.1 10.4] y [0.8 2.1 2.9 4.3 4.9 5.9 7.0 8.3 8.7 9.9] a. Solve for the regression line and report a and b. b. Plot the regression line overlaid with the sample data points c. Solve for the error term (residuals) and plot residuals vs....
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...
Below are given (a) A scatterplot of Y versus X and (b) A plot
of residuals versus fitted values after a simple linear regression
model was fit to the data. What is the equation of the fitted line?
Discuss what is indicated about the relationship between Y and X as
it relates to simple linear regression.
Fitted Line Plot Y = - 14.64 + 7.431 X R-Sq R-Sq (adj) 2.43700 91.9% 91.8% 1 > 20- 3 4 5 6 7...
Question 2: Suppose that we wish to fit a regression model for which the true regression line passes through the origin (0,0). The appropriate model is Y = Bx + €. Assume that we have n pairs of data (x1.yı) ... (Xn,yn). a) From first principle, derive the least square estimate of B. (write the loss function then take first derivative W.r.t coefficient etc) b) Assume that e is normally distributed what is the distribution of Y? Explain your answer...
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