Consider the following two statements about addingindependent variables into a regression model:1. Adding more independent variables into the modelnecessarily reduces bias.2. We do not necessarily have an omitted variable biasproblem if the omitted variable is uncorrelated with theincluded variable.Only statement 2 is true.Both statements are false.Only statement 1 is true.Both statements are true.

Bias is not always reduced by increasing the number of independent variables in the model: When we…

Answered: Consider the following two statements…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
Consider the following statements: I. Multicollinearity is present when there is a high degree of linear correlation between the residuals. II. A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: y-hat = 135 + 6x + errors. This implies that if the height is increased by 1 inch, the weight increases by 6 pounds in this linear model. a. I is true and II is false. b. I is false and II is true. c. Both I and II are true. d. Both I and II are false. e. More information is needed for each statement in order to tell which is true or false.
Which of the multivariate regression parameters listed below would be best interpreted as: the predicted value on the dependent variable when all of the independent variables in the model are equal to zero. a b1 X1 R2
In a data set with 12 observations, you try fitting two regression models. The esti-mated models are summarized as: Model 1: Y(hat) =3.5 + 2x; SSR= 5, and SSE= 10;Model 2: Y(hat) =3.0 + 1.5x + 0.4^2; SSR=23, and SSE=7 (a) Calculate R2 for both models. b. for both models test the null hypothesis that all the regression coefficients other than the intercept are 0.
A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.
Consider the following model:? = ?? + ?,known as the Classical Linear Regression Model (CLRM), where y is the dependent variable, X is the set of independent variables, ? is the vector of parameters to be estimated and ? is the error term. Present and discuss the R2 and the adjusted R2. Discuss pros and cons of each of the two statistics.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states, where xx is thousands of automatic weapons and yy is murders per 100,000 residents. xx 11.3 8.2 7.1 3.7 2.9 2.2 2.1 0.6 yy 13.9 10.7 10.3 7.2 6.5 5.6 5.5 4.6 Use your calculator to determine the equation of the regression line and write it in the y=ax+by=ax+b form. Round to 2 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 4.6 thousand automatic weapons? Round to 3 decimal places. According to this model, how many murders per 100,000 residents can be expected in a state with 4.4 thousand automatic weapons? Round to 3 decimal places.
Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.
Do students with higher college grade point averages (GPAs) earn more than those graduates with lower GPAs?† Consider the following hypothetical college GPA and salary data (10 years after graduation). GPA Salary ($) 2.22 72,000 2.27 48,000 2.57 72,000 2.59 62,000 2.77 86,000 2.85 96,000 3.12 133,000 3.35 130,000 3.66 157,000 3.68 162,000 #1) Use these data to develop an estimated regression equation that can be used to predict annual salary 10 years after graduation given college GPA. (Let x = GPA, and let y = salary (in $). Round your numerical values to the nearest integer.) ŷ = #2) Find the value of the test statistic. (Round your answer to two decimal places.) #3)Find the p-value. (Round your answer to three decimal places.) p-value =
In a laboratory experiment, data were gathered on the life span (y in months) of 33 rats, units of daily protein intake (x1), and whether or not agent x2 (a proposed life-extending agent) was added to the rats' diet (x2 = 0 if agent x2 was not added, and x2 = 1 if agent was added). From the results of the experiment, the following regression model was developed:ŷ = 36 + .8x1 − 1.7x2Also provided are SSR = 60 and SST = 180.The test statistic for testing the significance of the model is _____. a. 5.00 b. .50 c. .25 d. .33
The personnel director of a large hospital is interested in determining the relationship (if any) between an employee’s age and the number of sick days the employee takes per year. The director randomly selects ten employees and records their age and the number of sick days which they took in the previous year. Employee 1 2 3 4 5 6 7 8 9 10Age 30 50 40 55 30 28 60 25 30 45Sick Days 7 4 3 2 9 10 0 8 5 2 The estimated regression equation and the standard error are given. Sick Days=14.310162−0.236900(Age) Se=1.682207 Find the 95% prediction interval for the average number of sick days an employee will take per year, given the employee is 34 . Round your answer to two decimal places.
The following table shows data for the cost of natural gas in Maryland (in dollars per Million Btu) for x years since 1990. Year x Price in $ per Million Btu 1990 6.31 1991 6.14 1992 6.32 1993 6.75 1994 6.8 1995 6.34 1996 7.46 1997 8.12 1998 8.04 1999 8.25 2000 9.58 2001 11.28 2002 9.25 a. Define the explanatory and response variables for this problem. b. Use the calculator to obtain the linear regression line of best fit for the original prices; round to three decimal places. Write this prediction equation in the form: a. In a brief sentence, interpret the slope in the context of the problem.

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