N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
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If you are going to use software to solve the problem, use only R please.
Could you also include explanations of what you did in each steps?
Thank you.
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Solved in 1 steps
- 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.A random sample of 102 observations is selected to estimate the relationship between the price of a used car (y) and its odometer readings (x). The estimated simple regression line is: ý = 6533 – 0.03x (0.004) where the value 0.004 in bracket is the standard error of the point estimator for the slope in the regression model. Question 15. What percent of the variability of the used car values can be explained using this model? O 60% O 36% O 80% O 64% O 95% O o o o10) A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-0.767 b=31.009 r2=0.609961 r=-0.781 Use this to predict the number of situps a person who watches 7.5 hours of TV can do (to one decimal place)
- Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. The decrease in blood pressure y will vary about this subpopulation mean. What is the distribution of y for this subpopulation?When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errors tend to underestimate the sampling variation in the B;? Is it always true that the OLS standard errors are too small?find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. In each case, there is sujficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Altitude and Temperature Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
- The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use he regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Redshift 0.0233 0.0543 0.0716 0.0396 0.0436 0.0107 Distance 0.34 0.74 0.99 0.56 0.62 0.12 a. Find the explained variation. Round to six decimal places as needed.)This table reports the regression coefficients when the returns of the size-institutionalownership portfolio (columns 1 and 2) returns are regressed on three variables: a constant(column 3), the stock market returns (column 4), and the change of the value weighted discountof the closed end fund industry (column 6). Columns 5 and 7 report the corresponding t-statistics of the coefficient estimates. Note that a t-statistic with an absolute value above 1.96means the coefficient estimate is significantly different from 0 at the 1% level. Column 8reports the R square of the regressions. Column 9 reports the mean institutional ownership ofeach portfolio. The last column reports the F-statistics for a multivariate test of the null hypothesis that the coefficient on ΔVWD in the Low (L) ownership portfolio is equal to theHigh (H) ownership portfolio. Two-tailed p-values are in parentheses. 1. What is the main finding of this Table? 2. What is the explanation for…Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. What is the subpopulation mean when x = 7 servings per day?
- The following estimated regression equation based on 10 observations was presented. ŷ = 29.1270 + 0.7906x1 + 0.3980x2 (a) Develop a point estimate of the mean value of y when x1 = 190 and x2 = 350. (b) Develop a point estimate for an individual value of y when x1 = 190 and x2 = 350. (2) The admissions officer for a certain college developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high school GPA. ŷ = −1.38 + 0.0234x1 + 0.00482x2 where x1 = high-school grade point average x2 = SAT mathematics score y = final college grade point average. (a) Interpret the coefficients in this estimated regression equation. (b) Predict the final college GPA for a student who has a high-school average of 83 and a score of 530 on the SAT mathematics test.For each gender, estimate an earnings regression where the dependent variable is Annual Earnings and the independent variable is Age. Report the results for each regression, and provide an interpretation of the coefficient associated with age. Female- annual earning: 49347.58 age: 42.81 education: 14.4 Male- Annual earning: 69984.54 age: 42.86 education: 14.11.In a partially destroyed laboratory, record of an analysis of correlation, data, the following results only are legible:Variance of X=9. Regression equation: 8X –10Y + 66=0, 40X–18Y = 214.(1) the mean value X and Y,(2) the correlation coefficient between X and Y, and (3) the standard deviation of Y ?