1.1 -- Which of the following assumptions is not needed for 3 to be an unbiasedestimate of the population parameter in the regression modely = a + B₁x₁ + B2₂x₂ + Uiwhere a is the intercept term, ß is the slope parameter, and u is the unobserved errorJerm?A. The variance of the error term is homoskedastic, i.e. var (u|x₁, x₂) = 0².B The variable, x₁ and x2, are mean independent of the error term. E[ulx₁, x₂] = 0. mC. No perfect collinearityD. We have a random sample of size n from the underlying population

Regression model: This statistical technique is used frequently in predictive statistics. It depicts…

Answered: 1. !--- Which of the following…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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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?
4. A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 122 132 145 161 178 190 x 8 10 12 14 16 18 (a) Test for the significance of regression using the analysis of variance with a = 0.05. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? (b) Estimate ². (c) Estimate the standard error of the slope and intercept in this model. (d) Test the hypothesis that the increase in the speed of 1 km/h results in the runner's heart rate average increase of 7 points at a = 0.05. Suppose that the alternative hypothesis is that the average increase of the runner's heart rate in this situation does not equal 7 points.
According to the nutrition research, recommendation on the consumption of fiber for children and teenagers is the following ( y is the amount of fiber per day (in grams), x is the age): y 21 24 26 28 29 33 | 38 43 44 2 4 6 8 10 12| 14 16 | 18 X 0.1. Can you conclude that the model specifies a (a) Test for the significance of regression using the analysis of variance with a = useful linear relationship between these two variables? We conclude that the model specifies a useful linear relationship at a = 0.1. (b) Estimate o?. Round your answer to three decimal places (e.g. 98.765). 2 %D (c) Estimate the standard error of the slope and intercept in this model. Round your answers to three decimal places (e.g. 98.765). se( B1) i se( B o) = i
22. You are given the following value from a t-table as needed: P(tı40 > 1.656) = 0.05 Association between student math and verbal scores on the SAT was modeled by a linear regression model using the output given below for sample scores for a graduating class from a high school. Variable Count Мean Verbal 142 596.296 Math 142 612.099 Dependent variable is Math R-square = 46.9% %3D s=71.75 with 142-2=140 df Variable Coefficient SE(Coeff) t-ratio P-value Intercept 209.554 34.35 6.1 <0.0001 Verbal 0.675 0.0568 11.9 <0.0001 Find a 90% prediction interval for the Math score of a graduating student that has a verbal score of 500.
11. For temperature (x) and number of ice cream cones sold per hour (y). (65, 8), (70, 10), (75, 11), (80,13), (85, 12), (90, 16). Interpret the coefficient of determination. Optional Answers: 1. 88.2% of the variability in the number of cones sold is explained by the least-squares regression model. 2. 93.9% of the variability in the number of cones sold is explained by the least-squares regression model. 3. 88.2% of the variability in the temperature is explained by the least-squares regression model. 4. 93.9% of the variability in the temperature is explained by the least-squares regression model.
Consider the following regression equation: Y, = Po + B,X, + Hip where X;, Y, þPo, B1, and u, denote the regressor, the regressand, the intercept coefficient, the slope coefficient, and the error term for the " observation, respectively. When would the error term be homoskedastic? A. The error term is homoskedastic if the variance of the conditional distribution of u, given X is constant for i= 1..n, and in particular does not depend on X, B. The error term is homoskedastic if the variance of the joint distribution of u, and Y, is constant for i= 1. n and in particular does not depend on Y- O C. The error term is homoskedastic if the variance of the conditional distribution of u, given Y is constant for i= 1.n, and in particular does not depend on Y O D. The error term is homoskedastic if the variance of the conditional distribution of u given X, is variable for i=1. n, and in particular depends on Xj. Which of the following statements describes the mathematical implications of…
(Prob. 11-27, p. 445) Consider the following computer output. The regression equation is Y= 12.9+2.34 x Predictor Coef SE Coef т Constant 12.857 1.032 ? X 2.3445 0.1150 S=1.48111 R-sq = 98.1% R-sq(adj) = 97.9% Analysis of Variance Source ss MS F P DF Regression 912.43 912.43 ? ? Residual error 8 17.55 ? Total 929.98 a. Fill in the missing information. You may use bounds for the P-values. b. Can you conclude that the model defines a useful linear relationship? c. What is your estimate of o?
Q. 5. Calculate regression equation by the method of least square and take deviation from actual mean from the following : x = 4 6 8. 10 12 y = 1 3 5 10 11
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 16 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 45/62, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 34000. From this information, what is the critical value needed to calculate the margin of error for a 95 percent confidence interval for one of the model coefficients? (a) 2.069 (b) 2.110 (c)…
A simple linear regression was established between two variables, and it was found that the F ratio was 2.32 (p-value = 0.204). Which one of the following statements is correct? O a The linear regression model is better than the mean Ob. The constant and the independent variable coefficient are zeros OC. The linear regression model is not significantly better than the mean Od. The linear regression model is not significantly different from zero
The image contains two graphs typical of the analysis of a simple linear regression model. It can be stated that: a. The variance of the errors seems constant b. The errors do not come from a normal distribution c. The linear model does not seem appropriate d. The residuals are close to the line and therefore there is normality in the data. Why? Thanks
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS

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