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Process Control Question
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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 19.02The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
- The return rates of crane (Tagak) in Bulacan was studied using regression analysis and this relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year) was established. The following regression equation was obtained: y = 31.9 – 0.34x. Based on this estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would: A. decrease by 0.34% B. increase by 34% C. increase by 3.4% D. decrease by 3.4%Solids (grams) obtained from a material as y, with respect to drying time (Hours) as x. Ten experiments were carried out to obtain the following observations: Table on the picture (a) Create a scatter diagram for the data. (b) Estimated regression model according to the data conditions. (c) Calculate Model Accuracy (R²) and Relationship Between Variables (r²)The return rates of crane (Tagak) in Bulacan was studied using regression analysis and this relationship between return rate (x: % of birds that return to the colony in a givenyear) and immigration rate (y: % of new adults that join the colony per year) was established. The following regression equation was obtained: y = 31.9 – 0.34x. Based on this estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would: A. increase by 3.4% B. decrease by 3.4% C. increase by 34% D. decrease by 0.34%
- The return rates of crane (Tagak) in Bulacan was studied using regression analysis and this relationship between return rate (x: % of birds that return to the colony in a givenyear) and immigration rate (y: % of new adults that join the colony per year) was established. The following regression equation was obtained: y = 31.9 – 0.34x. Based on this estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would:The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.8 + 0.3x, +4.5x,, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values for the values of the independent variables. x, = 70, x, = 8.6 The predicted volume is cubic feet. (Round to one decimal place as needed.)The table shows the average weekly wages (in dollars) for state government employees and federal government employees for 8 years. The equation of the regression line is y=1.410x−17.174. Complete parts (a) and(b) below.
- The relationship between yield of maize, date of planting, and planting density was investigated in an article. Let the variables be defined as follows. y = percent maize yield x = planting date (days after April 20) z = planting density (plants/ha) The following regression model with both quadratic terms where x₁ = x, X₂ = Z, X3 = x² and x4 = 2² provides a good description of the relationship between y and the independent variables. y =a +B₁x₁ + B₂X₂ + B3X3+B₁x₁ + e (a) If a = 21.07, B₁ = 0.653, B₂ = 0.0022, B3 = -0.0207, and B4 = 0.00002, what is the population regression function? y = 509 X (b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exact answer.) (c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)? The mean yield would be higher for [May 7 You may need to use the appropriate table in Appendix A to answer this question.A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?Consider the multiple regression model to investigate the relationship between the number of fishes (Y) per section of the stream and the following independent variables: dissolved oxygen (3 < oxy < 10, in mg/liter), maximum depth (1 < maxdepth < 8, in feet), and water temperature (5< temp < 20, in °C). The location of the stream was also considered (lowland and upland). Y-hat = 23.09 + 0.199*oxy + 0.3361*maxdepth +8.6730*temp + 3.8290* lowland. Which of the following is(are) TRUE about the estimated regression coefficient for location of the stream? 1. The location of the stream is a categorical variable, so it is represented by a dummy variable with upland stream as the reference variable. II. Holding other factors constant, the number of fishes in lowland is 3.8290 higher than upland streams. O A. I only O B. II only O C. Both I and II O D. Neither I nor II