Obtain regression curve of Y on X for the following distribution : y f (x, y) = +1 exp (l + x) y 1+x | : / 20
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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.bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
- Can the average rate of change of a function be constant?The table below shows a set of four regression results of the effect of student-teacher ratio on average test score. Note each column represents the estimates related to each regression. The numbers in parenthesis below the coeffcients are the standard errors. Also, assume all the variables are continuous. (3) Regressor Student-teacher ratio (STR) (1) (2) (4) -1.00 -0.890 -0.757 -0.967 (0.27) (0.23) (0.31) (0.24) STR^2 0.865 0.875 (0.24) (0.29) % English Leamers (EL) -0.122 -0.112 -0.095 -0.067 (0.033) (0.054) (0.036) (0.057) STR x EL -0.098 -0.09 36.89 (0.033) (0.023) (9.31) STR^2 x EL 34.7 (5.60) Intercept 700.2 700.4 659.6 870.2 (5.60) (5.70) (4.60) (4.30) Standard Error of the Regression (SER) 9.08 (Adjusted) R-Squared Number of Observations 9.09 8.64 8.57 0.473 0.478 0.594 0.892 420 420 420 420 Based on the results of this table, which of the following statements best describes how the results should be interpreted (consider only individual effects on joint effects)? Oa There are…Calculate the simple linear regression to determine if the amount of sleep (y) can be predicted by time spent on homework (x). Graph the relationship and determine, numerically, if there are any outliers. Interpret all results in a paragraph citing the appropriate statistics. Sleep in minutes (Y): 360,400,420,440,540,480,320,440,360,420,420,390,360,480,360,360,480,420,360,480,270,360,420,360,420 Homework in minutes (X): 30,45,60,15,75,120,80,60,100,45,60,50,60,120,60,60,60,60,90,180,165,90,60,60,90