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- 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 19.02Respiratory 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.The line of best fit through a set of data is Y = – 11.943 + 2.982x According to this equation, what is the predicted value of the dependent variable when the independent variable has value 100? ŷ = Round to 1 decimal place.
- The line of best fit through a set of data is ŷ = - 6.227 – 1.507x According to this equation, what is the predicted value of the dependent variable when the independent variable has value 10? Round to 1 decimal place.Q/ Consider the following four points to interpolate for y = f(3.2) using: 1.0 0.1111 2.0 0.0625 3.0 0.0400 4.0 0.0278 1. Direct Fit Substitution.A photoconductor film is manufactured at a nominal thickness of 25 mils. The product engineer wishes to increase the mean speed of the film and believes that this can be achieved by reducing the thickness of the film to 20 mils. Eight samples of each film thickness are manufactured in a pilot production process, and the film speed (in microjoules per square inch) is measured. For the 25-mil film, the sample data result is.x₁ = 1.15 and S₁ = 0.11, while for the 20-mil film, the data yield 2 = 1.06 and s2 = 0.09. Note that an increase in film speed would lower the value of the observation in microjoules per square inch. Do the data support the claim that reducing the film thickness increases the mean speed of the film? Use a = 0.10 and assume that the two population variances are equal and the underlying population of film speed is normally distributed. The appropriate decision for the test is to reject the null hypothesis True False
- Q/ Consider the following four points to interpolate for y = f(3.2) using: 1.0 0.1111 2.0 0.0625 3.0 0.0400 4.0 0.0278A real estate agency collects the data in the following table concerning y = sales price of a house (in thousands of dollars) xl = home size (in hundreds of square feet) x2 = rating (an overall "niceness rating" for the house expressed on a scale from 1 [worst] to 10 [best], and provided by the real estate agency) Sales Price, Home Size, Rating, y (x $1000) X, (× 100 ft³) X2 180 98.1 173.1 136.5 23 11 20 17 141 15 8 165.9 21 4 193.5 127.8 163.5 172.5 24 13 19 25 The agency wishes to develop a regression model that can be used to predict the sales prices of future houses it will list. Use software of your choice to fit the 2 following models. Then answer the same questions (a-e) for both models. Modell: у %3 Во + Bix, + Bгх2 + € Model2: y = Bo + B1x1 + B2x2 + B3x² + e (a) Discuss why scatter plot of y vs x, and x2 indicate that this model might be reasonable. (b) Interpret the regression coefficients (c) Test significance of each individual coefficients. (d) Test overall regression…Consider the model y=-2.45x+7.18 derived from data between x=4 and x=10. What value of x represents interpolation of the data?