Question

In simple linear regression, the method of least squares determines the line that minimizes the sum...

In simple linear regression, the method of least squares determines the line that minimizes the sum of squared deviations between the observed y values and: a. the average of the y values b. the average of the x values c. the fitted line d. the line of residual errors

Homework Answers

Answer #1

In simple linear regression, the method of least squares determines the line that minimizes the sum of squared deviations between the observed y values and the fitted line.

In a cause and effect relationship, the independent variable is the cause, and the dependent variable is the effect. Least squares linear regression is a method for predicting the value of a dependent variable Y, based on the value of an independent variable X.

The method of least squares estimates the parameters by minimizing the sum of squares of difference between the observations and the line in the scatter diagram.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use the table below to find a least-square regression line, and then compute the sum of...
Use the table below to find a least-square regression line, and then compute the sum of the squared residuals for the least-squares regression line. You can use calculator or formula. x 3 5 7 9 11 y 0 2 3 6 9 A Linear regression: y ̂ = -3.7x + 1.1 ; Sum of squared residual: 1.6 B Linear regression: y ̂ = 1.1x – 3.7 ; Sum of squared residual: 1.6 C Linear regression: y ̂ = 1.1x +...
Select all the statements that are true of a least-squares regression line. 1. R2 measures how...
Select all the statements that are true of a least-squares regression line. 1. R2 measures how much of the variation in Y is explained by X in the estimated linear regression. 2.The regression line maximizes the residuals between the observed values and the predicted values. 3.The slope of the regression line is resistant to outliers. 4.The sum of the squares of the residuals is the smallest sum possible. 5.In the equation of the least-squares regression line, Y^ is a predicted...
For the data set below, (a) Determine the least-squares regression line. (b) Compute the sum of...
For the data set below, (a) Determine the least-squares regression line. (b) Compute the sum of the squared residuals for the least-squares regression line. x 20 30 40 50 60 ___________________ y 106 95 82 70 54 (a) Determine the least-squares regression line. ^ y =[]x +[] ( round to four decimal places as needed.)
Application of the least squares method results in values of regression model parameters that minimize the...
Application of the least squares method results in values of regression model parameters that minimize the sum of the squared deviations between the​ observed values of the independent variable and the predicted values of the dependent variable. observed values of the dependent variable and the predicted values of the independent variable. observed values of the independent variable and the predicted values of the independent variable. observed values of the dependent variable and the predicted values of the dependent variable.
Showing that residuals, , from the least squares fit of the simple linear regression model sum...
Showing that residuals, , from the least squares fit of the simple linear regression model sum to zero
Which of the following is TRUE in simple linear regression? A. A residual represents the difference...
Which of the following is TRUE in simple linear regression? A. A residual represents the difference between an observed Y value and predicted X value for a given Y value. B. A residual is always greater than the observed Y value. C. A residual represent the difference between the average X value and the average Y value. D. None of the above.
A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from...
A least-squares simple linear regression model was fit predicting duration (in minutes) of a dive from depth of the dive (in meters) from a sample of 43 penguins' diving depths and times. Calculate the R-squared value for the regression by filling in the ANOVA table. SS df MS F-statistic Regression Residual 1182.955 Total 537814.901 0.91 0.0902 0.0022 4.92461123041641e-23
Consider the simple linear regression model and let e = y −y_hat, i = 1,...,n be...
Consider the simple linear regression model and let e = y −y_hat, i = 1,...,n be the least-squares residuals, where y_hat = β_hat + β_hat * x the fitted values. (a) Find the expected value of the residuals, E(ei). (b) Find the variance of the fitted values, V ar(y_hat ). (Hint: Remember that y_bar i and β1_hat are uncorrelated.)
1. The least squares criterion, SSE, SSR, and SST In the United States, tire tread depth...
1. The least squares criterion, SSE, SSR, and SST In the United States, tire tread depth is measured in 32nds of an inch. Car tires typically start out with 10/32 to 11/32 of an inch of tread depth. In most states, a tire is legally worn out when its tread depth reaches 2/32 of an inch. A random sample of four tires provides the following data on mileage and tread depth: Tire Mileage Tread Depth (10,000 miles) (32nds of an...
The least squares method requires that the variance ? 2/? of the error variable ? is...
The least squares method requires that the variance ? 2/? of the error variable ? is a constant no matter what the value of x is. When this requirement is violated, the condition is called: A. heteroscedasticity B. non-independence of ?ϵ C. homoscedasticity D. influential observation In regression analysis, the coefficient of determination ?2 measures the amount of variation in y that is: A. unexplained by variation in x B. explained by variation in x C. caused by variation in...