It can be shown that the LS estimators areΣ₁(Yt - Ý)(t – t)Σ1(t – i)2B₁ = 3. For a time series with linear trend i.c. Y = Bo + B₁t + Ct, verify the least squaresestimators for ₁ on slide 12.

Yt=β0+β1t+ϵtWe have to verify the least square estimator of β1

Answered: t can be shown that the LS estimators…

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 1E

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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?
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.
6. The weather in San José is either sunny or rainy. Suppose that, after a sunny day, there is a 30% chance of having a rainy day, and after a rainy day, there is a 50% chance of having a sunny day. (a) Construct a difference equation model to predict the weather, where Sn is the chance of the nth day being sunny, and Rn is the chance of the nh day being sunny. (b) Suppose today is sunny. What is the probability that the day after tomorrow is sunny? (c) Compute the fixed point for the system. (d) Interpret the fixed point in terms of the long-term behavior of the system.
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?
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?
Suppose that we want to build a model that predicts the group membership of a hurricane, either tropical (0) or non-tropical (1) based on the latitude of formation of the hurricane. The response variable is the binary variable Type.new (type of hurricane) and the predictor variable is FirstLat (First Latitude). Using R, we build a model by applying the glm () function. For the logistic regression model, we specify family = "binomial". The data is available at https:/userpage.fu-berlin.de/soga/200/2010_data_sets hurricanes.xlsx. The R code is set up filename my.filename |z|) * (Intercept) -9.08263 *# FirstLat # --- * Signif. codes: -9.446 9.447 <2e-16 **. <2e-16 **. 0.96148 0.37283 0.03947 0 *** 0.001 ** 0.01 * 0.05 '. 0.1 '1 *# (Dispersion parameter for binomial family taken to be 1) on 336 degrees of freedom on 335 degrees of freedom Null deviance: 463.11 # Residual deviance: 232.03 # AIC: 236.03 ** Number of Fisher Scoring iterations: 6 Which of the following is the correct model? I.…
When there is autocorrelation in time series variables, OLS regression models produce unreliable results because the regressions are not statistically significant. the errors of the regression are not independent of each other. the values of the dependent variable are not normally distributed.
Otitis media is a disease that occurs frequently in the firstfew years of life and is one of the most common reasonsfor physician visits after the routine checkup. A study wasconducted to assess the frequency of otitis media in thegeneral population in the first year of life. Table 4.15 givesthe number of infants of 2500 infants who were first seen atbirth who remained disease-free by the end of the ith monthof life, i = 0, 1, . . . , 12. (Assume no infants have been lostto follow-up.) Disease-free infants ati the end of month i0 25001 24252 23753 23004 21805 20006 18757 17008 15009 130010 125011 122512 1200 Suppose an “otitis-prone family” is defined asone in which at least three siblings of five develop otitis media in the first 6 months of life. What proportionof five-sibling families is otitis prone if we assume thedisease occurs independently for different siblings in afamily?
Compute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)
An environmental chemist is performing a study of iron in atmospheric particulate measured downwind from a steel mill. She is concerned that wind velocity at the time of measurement may affect the readings. So, she decided to obtain observations on 30 randomly chosen days during the period of peak operation of the mill. She then, compares measurements taken on days when the wind is calm (velocity ≤ 5 knots) with measurements taken on windy days (velocity > 5 knots). The data are presented as the following: Table 1: Measurement of iron Calms Days Windy Days 0.68 0.74 0.88 0.25 0.29 0.3 0.43 0.45 0.5 0.89 0.97 1 0.65 0.91 0.92 0.93 0.95 1.01 1.17 1.25 1.27 0.69 0.74 0.8 0.87 0.87 0.89 8.85 1.54 0.6 1.03 1.16 By using SPSS or Minitab only: (1) Generate a descriptive table and summarize the data. (ii) Synthesize and discuss the different on the iron level between two days using boxplots. (iii) Propose the appropriate test to the study.
Assume a multiple linear regression y = Bo + B1 a1+ B2x2 + e. Which statement(s) is(are) true about the variance inflation factors (VIFS) of the coefficient estimates b1 and b2 ? I. The VIF of b, is the same as the VIF of b2. II. VIF will likely be large if X2 is highly positively correlated with X1 II. VIF will likely be large if X2 is highly negatively correlated with X1 IV. VIF will likely be close to 1 if X1 and X2 are independent O l and IV 1, II, III and IV Il and III OIV only I only

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t can be shown that the LS estimators are Σ₁(Yt-Y)(t - t) Σ1(t − 1)2 B₁ =