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- The article “Models for Assessing Hoisting Times of Tower Cranes” (A. Leung and C. Tam, Journal of Construction Engineering and Management, 1999: 385–391) presents a model constructed by a stepwise regression procedure to predict the time needed for a tower crane hoisting operation. Twenty variables were considered, and the stepwise procedure chose a nine-variable model. The adjusted R2 for the selected model was 0.73. True or false: a) The value 0.73 is a reliable measure of the goodness of fit of the selected model. b) The value 0.73 may exaggerate the goodness of fit of the model. c) A stepwise regression procedure selects only variables that are of some use in predicting the value of the dependent variable. d) It is possible for a variable that is of no use in predicting the value of a dependent variable to be part of a model selected by a stepwise regression procedure.A random sample of 8 office staffs hired within the previous year was selected from a large corporation. For each selected office staff, his or her experience (in months) at the time of hire and starting salary were recorded. The data is given in the table below. Experience (in months) 13 6 8 10 20 7 9 15 Starting Salary (in thousand pesos) 20 14 16 19 21 12 13 21 Determine the following: regression equation sum of squares for error standard error coefficient of determinationUsing the regression line attached. Based on only the above plot, one can conclude: a) height causes an increase in weight b) weight causes an increase in height c) taller people are more likely to weigh more than shorter people, at least in the sample on which this data is based d) a statistically significant predictive relationship between height and weight e) c and d
- Following table shows the data of traffic density and accident ratio taken fromLahore Islamabad Motorway in the first quarter of 2018.Traffic Density X 30 35 40 45 50 60 70 80 90Accident Ratio Y 2 4 5 5 8 15 24 30 32a. Determine the equation for the estimated regression line of Y on Xb. Calculate the coefficient of determination.c. Find the product moment coefficient of correlationA research department of an American automobile company wants to develop a model topredict gasoline mileage (measured in MPG) of the company’s vehicles by using theirhorsepower and weights (measured in pounds). To do this, it took a random sample of 50vehicles to perform a regression analysis as follows: SUMMARYOUTPUTRegression StatisticsMultiple R 0.865689R Square 0.749417Adjusted RSquare 0.738754Standard Error 4.176602Observations 50ANOVAdf SS MS FRegression a 2451.973702 1225.987 dResidual b 819.8680976 cTotal 49 3271.8418CoefficientsStandardError t StatIntercept 58.15708 2.658248208 21.87797Horsepower -0.11753 0.032643428 -3.60028Weight -0.00687 0.001401173 -4.90349(a) State the multiple regression equation. Interpret the meanings of the coefficients forhorsepower and weight.(b) Test the validity of this multiple regression equation at the significance level of 1%. Showyour reasoning.(c) The research department claims that the weight of the vehicle is negatively linearly related…A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of regressions coefficients and write down the simple linear regression model.
- Give the data: Y. 12,14, 15, 17,18, 15,16 X1. 8,8,6,5,3, 4,7 X2. 0,1,1,2, 3,3,4 Obtain the least square estimates of the parameters in the multiple regression model and test the over all significance using Anova.A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 1. Predict the sales next month for an employee with 2.5 years of experience. The predicted sales is 8.6 cars. 2. Compute the coefficient of determination and interpret its meaning. The coefficient of determination is 0.234. 3. Do the sample data provide evidence that the model is useful for predicting average monthly sales for employees based on their sales experience using α=0.05? The test statistic is (Type an integer or decimal rounded to two decimal places as…Given the table below, Let y, x1, x2, and x3 be the time of concentration (t, in hr), watershed length (L in ft), watershed slope (S in %), and runoff curve number (CN): Evaluate the linear multiple regression model with two or three predictor variables. Compute the multiple correlation coefficient, the standard error of estimate, and the standard deviation of the variable y. Discuss the reliability of the model
- A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 0.203521 The coefficient of determination is 0.234 Test statistic= 0.704 P-value= 0.014 Construct a 95% confidence interval around the sample slope and interpret its meaning. The confidence interval is (__________,_________). (Type an integer or decimal rounded to three decimal places as needed.)A researcher wants to forecast the annual sales of Walmart, based on store size. To examine the relationship between the store size in square feet and its annual sales in million dollars, a sample of 14 stores was selected shown below in the image: Answer the following: i) Null hypothesis of correlation ii) Coefficient of Correlation and its interpretation iii) Interpret the sig value of ANOVA. iv) Coefficient of Determination and its interpretation v) Write down the Regression Model. vi) Interpret the value of ‘a’ vii) Interpret the value of ‘slope’Here is a bivariate data set. Find the regression equation for the response variable y. x y 60.9 36.2 55.8 44.3 27.8 61.7 36.1 56.3 56 53.7 49.8 55.2 45.7 51.5 60.1 46.6 63.1 50 63.9 40.2 68.8 45.4 32.3 60.4 76.6 40.6 65.4 46 65.6 42.7 regression equation: Enter the equation in slope-intercept form with parameters accurate to three decimal places.
