7. Consider the simple linear regression given byY₁ =B1+ B2X+uiBut instead of assuming E(u|x) = 0, suppose one assume E(u|x) = 3 ObtainOLS estimator B1,B2.

When the error term has a non-zero conditional mean, the standard assumptions of the classical…

Answered: 7. Consider the simple linear…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 8PT: Does Table 1 represent a linear function? If so, finda linear equation that models the data.

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The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
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?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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.
Does Table 1 represent a linear function? If so, finda linear equation that models the data.
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?
3. Derive the solution for the estimated intercept (₁) in case of a univariate linear regression.
I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
Construct an example of a regression model that satisfies the assumptionE(ui | Xi) = 0 but for which E(U | X ) ≠0n.
If I add the additional condition which is the labor is female using the following: #People who is femalefemale = x*0.46 Will it become dependent variable and how will I do linear regression model by adding this condition?

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7. Consider the simple linear regression given by Y₁ =B1+ B2X+ui But instead of assuming E(ur) = 0, suppose one assume E(u|x) = 3 Obtain OLS estimator B1,B2.