Problem 2. Show that D; = (DFFITS;)² MSE (₁) (p+1)MSE'
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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 average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.4 Let f(x) = (1/10)(x-3)^2 for x = 1, 2, 3, 4, 5 %3D Find the standard deviation of X. For the instructor, this was question 11. / 1.8 X 3.1 X 3.4 X 3.5 X 9.4 X 12.4
- 9. (a) Explain the quickest method of finding the average price per kilo of wheat for 20 years when the given data gives the number of kilo per rupee for 10 years and the price in rupee per kilo for next 10 years. (b) and he gets a mileage of only 10 miles per gallon of gasoline. On the return trip he makes 15 miles per gallon. Find the harmonic mean of his mileage. Verify the fact that this is the proper average to use by assuming that the distance from A to B is 60 miles. A man motors from A to B. A large part of the distance is uphillUse the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2.Samples of size 105 from Population 1 with mean 94 and standard deviation 12 and samples of size 75 from Population 2 with mean 76 and standard deviation 15Round your answer for the standard error to two decimal places.standard error =The coefficients of variation for each data set are A, More than 5 percentage point apart B, Within 5 percentage points of each other Therefore, the systolic measurements vary A, Significantly less than B, Significantly more than c, about the same as
- 5. TRUE or FALSE: The residual value is the difference between the observed y- value and the predictedy- value, yˆ .Assume that you have collected cross-sectional data for average hourly earnings (ahe), the number of years of education (educ) and gender of the individuals (you have coded individuals as "1" if they are female and "0" if they are male; the name of the resulting variable is DFemme). Having faced recent tuition hikes at your university, you are interested in the return to education, that is, how much more will you earn extra for an additional year of being at your institution. To investigate this question, you run the following regression: ahe= -4.58 + 1.71×educ N = 14,925, R2 = 0.18, SER = 9.30 a. Interpret the regression output. b. Being a female, you wonder how these results are affected if you entered a binary variable (DFemme), which takes on the value of "1" if the individual is a female, and is "0" for males. The result is as follows ahe= = -3.44 - 4.09×DFemme + 1.76×educ N = 14,925, R2 = 0.22, SER = 9.08 Does it make sense that the standard error of the regression decreased…5. Suppose the number of days it takes you to get a flu shot after it is available follows this equation: Y₂ = 30 - 2X₁ where y, is the number of days until you get the flu shot, and X, is the number of people you know who have the flu. Further, suppose on average you know 2.3 people who have the flu, with standard deviation 5. Suppose that the population has size m = 10. (a) Find the average time until you get the flu shot after it is available. (b) Find the standard deviation of time until you get the flu shot after it is available. (c) What is EY;?
- A particular blood donation clinic accepted well over on hundred donors on Saturday. The length of time (in minutes) needed to draw a full donation of blood was recorded for 36 donors that day.. It was calculated that (x-x)2 = 84.72. What is the variance of the time it took the 36 donors to give blood that day? Round your answer to two decimal places.10. You estimated a regression with the following output. Source | SS df MS Number of obs = 333 -------------+---------------------------------- F(1, 331) = 4608.21 Model | 32636494.1 1 32636494.1 Prob > F = 0.0000 Residual | 2344225.8 331 7082.25316 R-squared = 0.9330 -------------+---------------------------------- Adj R-squared = 0.9328 Total | 34980719.9 332 105363.614 Root MSE = 84.156 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 30.79902 .4537022 67.88 0.000 29.90652 31.69153 _cons | 20.85313 42.1964 0.49 0.621 -62.1538 103.8601…Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2.Samples of size 110 from Population 1 with mean 92 and standard deviation 10 and samples of size 85 from Population 2 with mean 70 and standard deviation 17Round your answer for the standard error to two decimal places.