Explain why it can be dangerous to use the least-squares line to obtain predictions for x values that are substantially larger or smaller than those contained in the sample.The least-squares line is based on the x values ---Select---✓the sample. We do not know that the same linear relationship will apply for x values ---Select--- the range of values in the sample. Therefore the least-squares line should not be used for x values ---Select--- the range of values in the sample.

We have to explain:Why it can be dangerous to use the least-squares line to obtain predictions for x…

Answered: Explain why it can be dangerous to use…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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True or false. If the IQR of a dataset is 0 then any observation smaller than Q1 is classified as an outlier using the 1.5(IQR) rule.
Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…
A police academy has just brought in a batch of new recruits. All recruits are given an aptitude test and a fitness test. Suppose a researcher wants to know if there is a significant difference in aptitude scores based on a recruits’ fitness level. Recruits are ranked on a scale of 1 – 3 for fitness (1 = lowest fitness category, 3 = highest fitness category). Using “ApScore” as your dependent variable and “FitGroup” as your independent variable, conduct a One-Way, Between Subjects, ANOVA, at α = 0.05, to see if there is a significant difference on the aptitude test between fitness groups. Identify the correct symbolic notation for the alternative hypothesis. A. H0: µ1 = µ2 B. HA: µ1 ≠ µ2 ≠ µ3 C. H0: µ1 = µ2 = µ3 D. HA: µ1 ≠ µ2
Students in an AP Statistics class wanted to determine if a person's hand span is associated with the number of candies he or she can pick up from a bowl of candy. For the fourteen students in the class, each student's hand span and the number of candies he or she was able to pick up was recorded. A least- squares analysis was conducted on the number of candies versus hand span. The conditions for inference were checked and deemed reasonable. The regression analysis output is given in the table below. Predictor Constant Coef -8.74 SE Coef T P 10.81. -0.81 0.434 Hand span 1.26 0.52 2.44 0.031 S=3.34 R-Sq 33.1%
Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin; - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team==== "Brooklyn Nets" Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1 80 Coef. Std. Err. MS 81 206.320988 8.439024 3.049595 -5.219512 2.156389 1459.95122 190.65061 t Number of obs F (1, 80) Prob > F R-squared. Adj R-squared = Root MSE P>|t| 2.77 0.007 -2.42 0.018 82 7.66 0.0070 0.0874 0.0760 13.808 [95% Conf. Interval]…

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