Problem #4: (2 points) Find a 100(1 - a)% confidence interval for 0, given X₁,,X, i.i.d. with pdf f(x0) = 1,0-0.5 < x < 0+0.5. f(x10) = 2x/02, 0 < x < 0,0 > 0.
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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.Let the equations of the regression lines be expressed as 8X - 2Y = 0 and 3Y – 2X = 9 Then the correlation between X and Y is,A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
- Here, mean of X is 3 and the mean of Y is 7. The regression line that predicts Y from X necessarily goes through the point (3,7). True FalseSuppose 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.The line of best fit through a set of data isy=46.539+4.023xy=46.539+4.023xAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 40?y = Round to 1 decimal place.
- The line of best fit through a set of data is y = 60.638 – 0.836x || According to this equation, what is the predicted value of the dependent variable when the independent variable has value 190? y = Round to 1 decimal place.How would you calculate the stationary points of a multivariate function?A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x, = distance traveled (miles) and x, = the number of deliveries made. Suppose that the model equation is Y = -0.800 + 0.060x, + 0.900x2 + € (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? 5.8 v hr (b) How would you interpret ß1 = 0.060, the coefficient of the predictor X1? o When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a…
- Suppose a logistic regression model is fitted for the probability of car ownership for residents of a certain city in Oman (Y=1 if a resident owns a car, Y=0 if a resident does not own a car). Suppose the explanatory variables used are x1=no. of years a resident spent in schooling and x2 is gender of the resident of the city (x2=1 for a male and x2=0 for a female resident) a) Interpret el and e82 b) if BO= -1.6, B1=0.4 and B2=3, estimate the probability of a resident in the city owning a car.As the value of correlation coefficient increases from 0 to 1, or decreases from 0 to -1, how do the points of the scatter plot fit the regression line?(2) Sdr= 1 x=. V1-x2