The most common method of choosing the line that best summarises the linear relationship (or linear trend) between the two variables in a linear regression analysis, from the bivariate data collected. Show
Of the many lines that could usefully summarise the linear relationship, the least-squares regression line is the one line with the smallest sum of the squares of the residuals. Two other properties of the least-squares regression line are: Curriculum achievement objectives reference Problem 71 Multiple choice: Select the best answer for Exercises 71 to 78. Which of the following is not a characteristic of the least-squares regression line? (a) The slope of the least-squares regression line is always between 1 and 1. (b) The least-squares regression line always goes through the point (x , y ). (c) The least-squares regression line minimizes the sum of squared residuals. (d) The slope of the least-squares regression line will
always have the same sign as the correlation. (e) The least-squares regression line is not resistant to outliers. Step-by-Step Solution: Step 1 of 2 We have determine which statement is not a characteristic of the least-squares regression line: Other solutionsDiscover and learn what students are askingPeople also purchasedRelated chapters
Which of the following is not a characteristic of the least-squares regression line?a. The slope of the least-squares regression line is always between –1 and 1.b. The least-squares regression line always goes through the point (x¯,y¯) .c. The least-squares regression line minimizes the sum of squared residuals.d. The slope of the least-squares regression line will always have the same sign as the correlation.e. The least-squares regression line is not resistant to outliers.
The correct option is (a) The slope of the least-squares regression line is always between and Question: Video Answer:  Get the answer to your homework problem. Try Numerade free for 7 days DiscussionYou must be signed in to discuss. Video TranscriptSo while signal question, let's for a move to the answer colors he had. The correct option is B. The list is required. Regulation Line minimizes the sum of is quite vertical distance between the points on the line. So here is full definition of the question. That option B is correct. The list is quite. Regulation. Line minimizes the thumb of his quiet vertical distance between the points and the line. I hope you better understand the full definition. So for any further cure is in doubt. I am there for help. So thank you. Numerade has step-by-step video solutions, matched directly to more than +2,000 textbooks. Study Groups Study with other students and unlock Numerade solutions for free. Try Now Top Intro Stats / AP Statistics EducatorsIntro Stats / AP Statistics CoursesLectures Join Course Recommended Videos02:48 (a) Is the r.m.s. error of the line below around $0.1,0.3,$ or 1$?$ 01:36 Least-squares idea The table below gives a small set of data. Which of the following two lines fits the data better: $\hat{y}=1-x$ or $\hat{y}=3-2… 00:44 By looking at the equation of the least-squares regression line, you can see that the
correlation between 04:24 In Exercises 43–46, tell which type of regression is likely to give the most accurate model for the scatter plot shown without using a calculator.… Additional Mathematics questions02:10 You are testing $H_{0}: \mu=10$ against $H_{a}: \mu \neq 10$ based on an SRS… 02:11 Which of two brands (X or Y) of electric razor shaves closer? Researchers wa… 01:29 Which of the following is not a characteristic of the least-squares regressi… 00:55 The number of calories in a food item depends on many factors, including the… 04:23 An experiment that claimed to show that meditation lowers anxiety proceeded … 00:40 There are two common methods for measuring the concentration of a pollutant … 02:07 Professor Moore, who lives a few miles outside a college town, records the t… 01:51 The following Normal probability plot shows the distribution of points score… 01:37 A .300 hitter In baseball, a 0.300 hitter gets a hit in $30 \%$ of times at … 03:06 A gardener wants to try different combinations of fertilizer (none, 1 cup, 2… What are characteristics of the least squares regression line?1. The sum of the residuals is zero. 2. The point with x-coordinate equal to the mean of the x-coordinates of the observations and with y-coordinate equal to the mean of the y-coordinates of the observations is always on the least-squares regression line.
What is least about the least squares regression line?The Least Squares Regression Line is the line that minimizes the sum of the residuals squared. In other words, for any other line other than the LSRL, the sum of the residuals squared will be greater. This is what makes the LSRL the sole best-fitting line.
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Calculating the Least Squares Regression Line.. What are the assumptions of the least squares regression line?7 OLS regression assumptions. The regression model has linearity in its error term and coefficients. ... . The error term's population mean is zero. ... . There are no correlations between the independent variables and the error term. ... . Each observation of the error term is independent of others. ... . The error term's variance is constant.. Is the least squares regression line resistant to outliers?Note Least squares regression is not resistant to the presence of outliers. A (single) leverage point completely determines the line, although there is no variation at all in X, with one exception.
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Which of the following is not a characteristic of the least-squares regression line?
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