2. We will show a link between regression and the T-test. Suppose we have data of written ofthe form (Yij, xj), equal to,(Y11, 1), (12, 1), (Yin, 1)(Y21, 1), (22,-1),..., (2n-1)And assume the model,Yij = Bo+B₁xj + Eij, where Eijid N(0.02)(a) Show that Bo Y. :===+Y=-12.2n(b) Show for the fitted values, Y₁₁ = Y₁., and Y2j= Y2. for 1jn(c) Show that ²= 82 for the pooled variance t-test(d) Show that the test statistic for the hypothesis test Ho₁ = 0, HA: B00 can bewritten as,Y₁. - Y2.TAnd therefore the pooled variance T-test can be written via the SLR equation

References Chambers, J. M., & Hastie, T. J. (2017). Statistical models. In Statistical models in…

Answered: 2. We will show a link between…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Which pair of data points are always on the regression line: Y = a + bx? (0, 0) (0, b) (X, Y) (a,0)
A) A linear regression has a =6 and b=5 what is y predicted as when x=9? B) A linear regression has b=3 and a=4.What is the predicted Y for x=7?
a) explain on he strenght and variation of the model (multiple regression) b) At a-value =0.01. test whether there is a significiant relationship between the dependent variable (y) and the independant variables x1, x2 and x3
If the points (x1, y1), (x2, y2),..., (xn, yn) lie on a straight line, what can you say about the regression line associated with these points?
The number of murders and robberies per 100,000 population for a random selection of states are shown. Find the equation of the regression line y'=ax+b, and predict the number of robberies when x=4.5 murders murders,x: 2.4,2.7,5.6,2.6,2.1,3.3,6.6,5.7 robberies,y : 25.3,14.3,151.6,91.1,80,49,17.3,45.8
We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form yˆ=b0+b1x1+b2x2 HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars.
Let the equations of the regression lines be expressed as 8X - 2Y = 0 and 3Y – 2X = 9 Then the correlation between X and Y is,
Assume that we have the usual Simple Linear Regression model given by: Y₁ = Bo + Bixi +8 Show that in this case: Where Txy R² = rzy is the correlation coefficient between x and y.
A study tests the effect of earning a Master's degree on the salaries of professionals. Suppose that the salaries of the professionals (S,) are not dependent on any other variables. Let D, be a variable which takes the value 0 if an individual has not earned a Master's degree, and a value 1 if they have earned a Master's degree. What would be the regression model that the researcher wants to test? A. S,= Po + B,D,+u, i=1, .. , n. O B. S,= Po + B, + u, i= 1, .. , n. OC. 1=6o +B1,S, + u, i= 1, .. , n. O D. 0=Bo +B, S, + u,, i= 1, .. , n. Suppose that a random sample of 160 individuals suggests that professionals without a Master's degree earn an average salary of $59,000 per annum, while those with a Master's degree earn an average salary of $80,000 per annum. The OLS estimate of the coefficient B, will be $ and that of B, will be $ Click to select your answer(s). DELL
We wish to predict the salary for baseball players (y) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2. HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Miquel Cabrera 108 38 28.050 Yoenis Cespedes 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez 111 30 22.750 Justin Upton 87 31 22.125 Adrian Gonzalez 90 18 21.857 Jason Heyward 49 7 21.667 Jayson Werth 70 21 21.571 Matt Kemp 108 35 21.500 Jacoby Ellsbury 56 9…

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