1. Test for relative extrema and saddle points. z=x²+ 10xy +y²+ 192x
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- For10 observations on supply (X) and price (Y) the following data are obtained ΣΧ-130, ΣΧ-2280, ΣΥ-5506 , ΣΧΥ-3467, ΣΥ-220 Obtain regression line Y on X and estimate supply when price is 16.Select the appropriate interpretation for the slope of the linear regression equation below. Y (Dependent Variable) = Grade Point Average X (Independent Variable) = Average number of hours spent using electronic devices for entertainment purposes yhat = 4 - 0.125*X A. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will increase on average by 0.125 points B. For every 1 GPA gained obtained by a student then on average that person will have watched 0.125 hours fewer of entertainment on electronic devices per week C. For every 1 GPA point lost by a student then on average that person will have watched 0.125 hours more of entertainment on electronic devices per week D. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will decrease on average by 0.125 pointsShort Answer 2 Show that if the regression model contains a constant regressor, then Ý = ", Ý.
- Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.Residual analysis is important when studying the potential for linear regression because it allows for assumptions to be ignored for a time while graphs are created. True O FalseThe 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.)
- An interaction term in a multiple regression model may be used when the coefficient of determination is small. there is a curvilinear relationship between the dependent and independent variables. neither one of 2 independent variables contribute significantly to the regression model. the relationship between X1 and Ychanges for differing values of X2.The slope, b represents * O predicted value of Y when X = 0. O the estimated average change in Y per unit change in X. O variation around the line of regression. O the predicted value of Y.The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant ŷ = 2.35+2.20X. Suppose, for a selected workstation, the labor input is 5, the predicted output is?
- Statistics professor wants to use the number of hours (x) a student studies for a statistics final exam to predict the final exam score (y). A regression model was fit based on data collected from a class during the previous semester, with the following results: (y hat): y = 35.0 + 3X What is the slope? a. Yb. 35.0c. 3d. XQ10. price based on two features. Suppose we are going to apply multivariate Linear Regression to predict the house x1 = age of the house (0 – 40) x2 = quality of neighbouring schools (0 – 3) h(8) = 0, + 8,x1 + 02x2 Suggest one way to scale the features. Describe what will happen if feature scaling is not performed before the training process is conducted.(15) 5. (TRUE, FALSE) In regression, the coefficient of determination gives the proportion of the variability in the dependent variable that is explained by the regression equation.