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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.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 scientist is calibrating a laboratory apparatus that will be used to measure the concentration of ozone in air samples. To check the calibration, samples of known concentration are measured. The true concentrations in ppm (x) and the measured concentrations in ppm (y) data points are: (0, 1), (10, 11), (20, 21), (30, 28), (40, 37), (50, 48), (60, 56), (70, 68), (80, 75), (90, 86), (100, 96). Because of random error, repeated measurements on the same sample will vary. The apparatus is considered to be in calibration if its mean response is equal to the true concentration. To check the calibration, the linear model y = ß0 + ß1 + ε is fit. Ideally, the value of ß0 should be 0 and the value of ß1 should be 1. A scientist is calibrating a laboratory apparatus that will be used to measure the concentration of ozone in air samples. To check the calibration, samples of known concentration are measured. The true concentrations in ppm (x) and the measured concentrations in ppm (y) data…
- The deviation of each observation (x) from the mean of the predictor variable is positive for every point in what quadrants? * Y (2) 1) 3 4)A scientist is calibrating a laboratory apparatus that will be used to measure the concentration of ozone in air samples. To check the calibration, samples of known concentration are measured. The true concentrations in ppm (x) and the measured concentrations in ppm (y) data points are: (0, 1), (10, 11), (20, 21), (30, 28), (40, 37), (50, 48), (60, 56), (70, 68), (80, 75), (90, 86), (100, 96). Because of random error, repeated measurements on the same sample will vary. The apparatus is considered to be in calibration if its mean response is equal to the true concentration. To check the calibration, the linear model y = ß0 + ß1 + ε is fit. Ideally, the value of ß0 should be 0 and the value of ß1 should be 1. The least-squares estimate of the error standard deviation σ is closest to:A linear regression to quantify the salaries of the employees in a company is estimated, using the following variables: Y: the salary of the employee in 1000 SEK. Age: the age of the employee in years R: the categorical variable Education with 3 groups; Primary, Secondary, University. a)Write down a linear model with intercept for the variable Y based on Age and R, in which the Primary level of education is the reference category for the Education variable. b)Mention a test to see if the variable Age significantly improves the model fit?
- iris is a built-in R data set (data frame). This data set contains gives the measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica. We are interested in some descriptive statistics related to the Sepal.Width column of the data frame. We can access the data directly by using the assignment x <- iris$Sepal.Width (In R use ?iris for info on this dataset.)Remember: x <- iris$Sepal.Widtha.Calculate the sample median of x. b. Using the R quantile function, find the .80 quantile of x.(80th percentile) c. Calculate the interquartile range of x using R. d. Calculate the sample mean of x. e. Calculate a 4% trimmed mean for x. f. Calculate the sample variance of x. g. Calculate the sample standard deviation of x. h. What proportion of the x values are within 2.0 sample standard deviations from the sample mean i. Calculate the minimum…2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231The equations of the regression line between two variables are expressed as 2x-3y=0 and 4y-5x-7=0 a) identify which of two can be called regression line of Y on X and X on Y b) find the correlation coefficient c) find mean value of X and mean value of Y
