M10 a. Mathematically express the CLRM assumption that is potentially violated if we omit a relevantvariable from a regression model.b. Suppose we don't have variable X₂ in our data. If X'2 is a proxy for X₂, how would you use it?What needs to be true about X2 to elminate OVB in our regression?c. Suppose we don't have either X₂ in our data or a suitable proxy variable. We won't be able toeliminate OVB, but we could make some reasonable guesses about the nature of the bias. Howwould you attempt to do this?

Answered: Image /qna-images/answer/fcebd36e-5632-45f4-972c-8ce34c8ab08d.jpg

Answered: a. Mathematically express the CLRM…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 4E

See similar textbooks

Similar questions

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?
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
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?
Conduct a simple linear regression analysis using the following response and exploratory (x) variables. > set.seed(28) > x y<-22 + 3*x + rnorm (80) A. B. C. Create a regression model for y-x Write down the coefficients of this model. Comment on "whether the model is statistically significant" or not. Indicate the reason why.
Suppose Connie used regression to predict the height of a woman’s current boyfriend by using her own height as the explanatory variable. Height was measured in feet from a sample of 100 women undergraduates, and their boyfriends, at De La Salle Lipa. Now, suppose that the height of both the women and the men are converted to centimeters. The impact of this conversion on the slope is: the magnitude of the slope will change neither the sign nor magnitude of the slope will change the sign of the slope will change both the sign and magnitude of the slope will change
2. Consider the following regression model: Class Average; = Bo + B1 x 0ffice Hours; + Ui Class Average is the students' average grade in the class at the end of the term and Office Hours is the number of office hours held by the instructor over the entire term. A researcher who collects data and regresses Class Average against Office Hours finds that, surprisingly, B< 0. The OLS estimator, B, however, likely suffers from omitted variable bias because instructors who teach large introductory courses with many non-major enrollees, in which grades are relatively low, might hold more office hours than instructors who teach small upper level courses with few non-major enrollees, in which grades are relatively high. Because of this omitted variable bias, it is likely the case that B,. A) В) V A
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?
Which of the following represents the least-square regression line's equation? A. y = -a - bx B. y = a + bx C. y = a - bx D. y = -a + bx
5. Consider the following two simple regression models: Model I : Y, = B,+B,X, +H, Model II : Y,=a, +a, (X,- X)+v, (1) Derive the estimators for B, and a,. Are they the same? (2) Derive the estimators for B, and a, . Are they the same?
Ex.2. The relationship of a substance produced in a production center in terms of stiffness and robustness is being investigated. 10 pieces were selected from among the materials produced for this purpose. It has been tested for stiffness and robustness. The data are as follows. Find the regression equation for the relationship between X and Y.
Assume that there is a positive linear correlation between the variable R (return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.3t + 4.8. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?
The following data give the percentage of women working in five companies in the retail and trade industry. The percentage of management jobs held by women in each company is also shown. %Management 60 50 a. From the following select the appropriate scatter diagram for these data with the percentage of women working in the company as the independent variable. Scatter diagram a 40 -30 20 10 20 Scatter diagram b %Management -60 50 -40 30 20 10 20 Scatter diagram c -60 %Management 50 10 -40 30 20 10 10 30 10 20 30 40 5,0 Scatter diagram c 40 50 60 %Working 6,0% Working 3,0 4,0 50 60%Working % Working % Management 68 46 74 54 61 50 22 65 48 34

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

Cengage Learning

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781305652224

Author:

Charles P. McKeague, Mark D. Turner

Publisher:

Cengage Learning

Functions and Change: A Modeling Approach to Coll…

Algebra

ISBN:

9781337111348

Author:

Bruce Crauder, Benny Evans, Alan Noell

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS