Consider the following estimated regressionIn Y, = 2.57 + 0.212 InK: + 0.343 InL: + 0.030 InWt(2.90) (0.348)(0.551)(0.063)where Y: is the industry output, Kt and Lt represent capital and labor, respectively. It isclaimed that there is no problem with the estimated regression and all the inferences areconsistent with economic theory.Is it true/false/ uncertain. Explain.ww w ww w ww m

Isider the following estimated regression In Y, = 2.57 + 0.212 InKt + 0.343 InLt + 0.030 InWt (2.90) (0.348) (0.551) (0.063) Yt is the industry output, Kt and Lt represent capital and labor d that there is no problem with the estimated regression and all ent with economic theory.

Isider the following estimated regression In Y, = 2.57 + 0.212 InKt + 0.343 InLt + 0.030 InWt (2.90) (0.348) (0.551) (0.063) Yt is the industry output, Kt and Lt represent capital and labor d that there is no problem with the estimated regression and all ent with economic theory.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section: Chapter Questions

Problem 30PT: For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or...

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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
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.
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
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?
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.
You spilled water on your calculations from (a) and can't remember what your estimated regression parameters are. But you do have two possible estimated errors for each of your initial four observations:
Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?
b) Consider the following regression model; = 24.7747 +0.9415X2i +0.0424X31 (6.7525) (0.8229) t = (3.6690) (1.1442) (0.5261) R² = 0.9635 R = 0.9531 df =7 RSS = 8,565.5541 ESS = 324.4459 (0.0807) where X₂ = income; X3 = wealth and Y= consumption (i) How would you interpret the model? (ii) Is there multicollinearity in the regression? How do you know?
A study wants to access the relationship between volume and weight of batch of logs of wood (100 logs). It turns out that the scale used to measure the weight is not working appropriately, and every time a log of wood is measured, the next mesaurement will be 1 lb more than it should be (eg. for the 10th log, the scale will read 10 lb more than their actual weight). Identify the assumption of regression that would be violated in this situation. If the experiemnters figured out this problem at the 100th measurement, can anything be done such that the data might still be used?
Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1=married, 0=otherwise), a dummy variable for head of household (Head: 1=yes, 0=no) and a dummy variable for management position (Manager: 1=yes, 0=no). We shall call this Model 1. The coefficient of partial determination (R2Yj.(All variables except j)) of each of the six predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given. Refer to model 1. Which of the following is the correct null hypothesis to test…
The chief of the emergency response services claims that their team responds to emergency distress calls within a 5 km radius in 360 seconds. An independent investigator wishes to test whether or not the presence of a thousand extra cars within the 5 km radius affects the emergency response time by 9.54 seconds. He randomly selects 100 distress calls and estimates the following regression: Question Help Y; = 370+0.26X;, where Y, denotes the predicted response time measured in seconds for the " emergency call and X, denotes the number of cars (in thousands) on the road within a 5 km radius at the time of the " emergency call. If B, is the slope coefficient, which of the following options states the investigator's null and alternative hypotheses? O A. Ho: B1 = 9.54 and H, B1 #9.54. B. Ho B1 =0.26 and H,: B, #0.26. OC. Ho B1 > 9.54 and H, B, 9.54. OD. Ho B>0.26 and H, ß, <0.26. Suppose taci associated with the test the investigator wishes to conduct is 1.98. The p-value will be (Round…
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X,), the annual income of the family (X,), and the number of times the family went out on an outing in the last year (X). She collects data from 152 families and estimates the following regression: Y = 120.45 + 1.12X, + 2.12X2 + 1.98X3 Suppose B1. B2, B3, denote the population slope coefficients of X, X2, and X3, respectively The researcher wants to check if neither X, nor X, have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions (Ho: B, = 0, B2 = 0 vs. H B, 0 and/or Bz 0) to be 3.00. The p-value for the test will be (Round your answer to two decimal places.) At the 10% significance level, we will the null hypothesis. reject fail to reject Enter your answer in…