For an AR(1) model with Y₁ = 7.5, = -0.6, = 5, and o² = 1, (a) Find Ŷ(1), (2), and Ŷ(6). (b) Find the error variances for your forecasts above.
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- 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.Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4For a MR model with 4 predictors, we have: SSE 288 and SST = 957 What percentage of the variation in Y is accounted for by its assumed relationship with the predictors?
- The intercept is 0, the autoregressive coefficient is 0.2 and the moving average coefficient is 0.5 in an ARIMA(1,1,1) model. What is the one-step ahead forecast if the shock for the current period is -2 and the current and one-period lagged values of the forecast variable are 110 and 105?For an AR(1) model with Yt = 7.5, o = -0.6, H = 5, and o? =1, (a) Find Ý:(1), Ÿ:(2), and Ý(6). (b) Find the error variances for your forecasts above.For an AR(1) model with Y = 7.5, o = -0.6,= 5, and o? = 1, %3D %3D %3D (a) Find Y:(1), Ý(2), and Ý:(6). (b) Find the error variances for your forecasts above.
- A study was undertaken to determine whether there was a significant weight (in lb) loss after one year course of therapy for diabetes, and whether the amount of weight (in lb) loss was related to initial weight. The following table gives the initial weight (x) and weight after one year of therapy (y) for 16 newly diagnosed adult diabetic patients.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:The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is
- Q- The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: (a) Estimate the linear regression line. (b) Estimate the final examination grade of a student who received a grade of 85 on the midterm report. (c) Find coefficient of correlationThe equation of the LSRL for the points on a scatterplot is ŷ = 5.3-0.23x. What is the residual for the point (5, 4)?The following regression uses data on illegal downloading of music. A sample of 500 individuals were asked whether they had downloaded music illegally (theft). In addition, respondents also gave answers to the following; caught: a respondent's belief of her chances of getting caught if she attempted to act illegally (0-10, 10 being "great risk") penalty: a respondent's belief regarding how severe her penalty would be if she got caught (0-10, 10 being “great risk) gender: gender, where male is 1 and female is 0 Edu: years of formal education Income: Income of the respondent (£) a. The estimated model was Theft = Bo + B1 caught + B2penalty + B3gender + B4Income + B5Edu Provide an explanation of the expected signs of each of the coefficients, referring to relevant economic theory.