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- What is the stability of the 4 equilibrium points? Does point (0,0) even count?In a study of the lung function of children, the volume of air exhaled under force in one second is called FEV1. (FEV1 stands for forced expiratory volume in one second.) Measurements were made on a group of children each year for two years. A linear model was fit to predict this year’s FEV1 as a function of last year’s FEV1 (in liters), the child’s gender (0 = Male, 1 = Female), the child’s height (in m), and the ambient atmospheric pressure (in mm). To try to improve the prediction of FEV1, additional independent variables are included in the model. These new variables are Weight (in kg), the product (interaction) of Height and Weight, and the ambient temperature (in °C). The following MINITAB output presents results of fitting the model FEV1 = β0 + β1 Last FEV1 + β2 Gender + β3 Height + β4 Weight + β5 Height · Weight + β6 Temperature + β7 Pressure + ε a) The F statistic is? b) How many degrees of freedom does the F statistic have? c) Find the P-value for the F statistic. Is the…Data were collected from a group of senior citizens, ages 65 and older, about their age and pet ownership. The results were used to calculate the model ŷ = –0.24x + 18.48, where x represents the age in years and ŷ represents the predicted number of pets owned. If a 45-year-old is predicted to have more than 7 pets, would that be a reasonable use of the model? This is not reasonable because the prediction is based on someone outside the original population. This is reasonable because the model is based on real data. This is not reasonable because it is impossible to own more than 7 pets. This is reasonable because the prediction is based on someone within the original population.
- In Step 2: Construct an estimated simple linear regression model how did you come up with the column X*X ?A) Compute the last-squares regression line for predicting US emission from NON US - emissions. b) If the non-US emission differ by 0.2 from one year to the next by how much would you predict the US- emission to differ?Here, mean of X is 3 and the mean of Y is 7. The regression line that predicts Y from X necessarily goes through the point (3,7). True False
- The correlation coefficient between the yearly returns of two mutual funds is 0.20. What does that mean about the strength and direction of the linear relationship between the returns of the two funds?The dove population on Honeydoom farms has become slightly invasive, doves have far out-competed the endangered Emerald Sparrows in the area – causing their near. The local animal control board would like to begin culling the dove population in order to ensure the survival of the Emerald Sparrow, but the control board will cease any culling when the population of sparrows and doves are equivalent, they will begin culling in one year. You believe that the current trends in population suggest that an equal dove to sparrow ratio can be expected in a fairly short period. You are asked for proof. Population growth can be modeled using the equation n(t)= n0e^rt where n0 is the initial population, is the rate of growth, and t is time in decades. Let us suppose we have a population of sparrows ns(t), with an initial population of ns0 and a population of doves nd(t), initial population of nd0, It has been observed that the doves decrease at a rate of 200 per year and the sparrows increase at…John Swanson, president of Market Research Inc., has asked you to estimate the coefficients of the modelY = β0 + β1X1 + β2X21 + b3X2where Y is the expected sales of office supplies for a large retail distributor of office supplies, X1 is the total disposable income of residents within 5 miles of the store, and X2 is the total number of persons employed in information-based businesses within 5 miles of the store. Recent work by a national consulting firm has concluded that the coefficients in the model must have the following restriction:b1 + b2 = 2Describe how you would estimate the model coefficients using least squares.
- A linear model has the equation y=10.4−0.25x. What is the residual for a point (6,9.2)? The residual is__.A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using two independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. With this regression model, the predicted price of a 10-year old home with 2,500 square feet of living area is __________. $205.00 $200,000.00 $205,000.00 $255,000.00Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when multiplying two numbers. x=80, y=60, ∆x= ∆y=5.
