solve 1a and b 1.See Data 1 in Bb. There are two variables. y: Tensile Strength (Psi) and x: Hardwood Concentration (%).Get scatter plot of y vs x. Explain their statistical relation. Based on the plot write a tentative regression model(you should not fit the model now, just write the model that you think is appropriate using B symbol and x.b.а.Consider Model 1: y=Bo+B,x + B,x²+ɛ. For Model 11.Test overall significance of the model using the F-test.2.Test the significance of adding x to the model that contains x². Also, test significance of adding x2 to themodel that contains x. Write a summary of your findings in this part.3.Would you retain B, in Model 1?Based on your findings in 1-3 above, choose Model 1 or a subset of Model 1 (Note: you should not fit allpossible subset models). For the model that you have selected (you should provide one final model that youthink is the "best", do not submit output for other models that you have tried), save St. Residuals, St. predictedvaluesС.y. Get apopriatplots and a p-value for Normality test of residuals. Does the model violate any ofthe assumptions: Functional form, Constant variance, and Normality?Now consider Model 2: y=Bo+B,x + B2x²+ B3x³ +ɛ. Which model would you prefer, Model 2, a subset of Model2 or the model you have selected in part (c)? Justify your answer by going through appropriate diagnostics.d. HardwoodConcentration* TensileStrength1.06.31.511.12.020.03.024.04.026.14.530.05.033.85.534.06.038.16.539.97.042.08.046.19.053.110.052.011.052.512.048.013.042.814.027.815.021.9

Let, x: Hardwood concentration (%). y: Tensile strength (Psi). Data: x y 1 6.3 1.5 11.1 2…

1. See Data 1 in Bb. There are two variables. y: Tensile Strength (Psi) and x: Hardwood Concentration (%). Get scatter plot of y vs x. Explain their statistical relation. Based on the plot write a tentative regression model (you should not fit the model now, just write the model that you think is appropriate using B symbol and x. b. а. Consider Model 1: y=Bo+ß1x + B2x²+ɛ. For Model 1 1. Test overall significance of the model using the F-test. 2. Test the significance of adding x to the model that contains x?. Also, test significance of adding x² to the model that contains x. Write a summary of your findings in this part. 3. Would you retain ß, in Model 1?

1. See Data 1 in Bb. There are two variables. y: Tensile Strength (Psi) and x: Hardwood Concentration (%). Get scatter plot of y vs x. Explain their statistical relation. Based on the plot write a tentative regression model (you should not fit the model now, just write the model that you think is appropriate using B symbol and x. b. а. Consider Model 1: y=Bo+ß1x + B2x²+ɛ. For Model 1 1. Test overall significance of the model using the F-test. 2. Test the significance of adding x to the model that contains x?. Also, test significance of adding x² to the model that contains x. Write a summary of your findings in this part. 3. Would you retain ß, in Model 1?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A marketing analysit is studying the relashionship between X = money spent on television advertising and Y = increase in slae. A simple linear regression model relates x and y as follows Y = 27.5 + 1.19 X What is the average change in sales associated with an additional 1 dollor spent on advertising? Group of answer choices A. For every additional 1 dollor spent on advertising, sales decreases by 1.19 dollars. B. For every additional 1 dollor spent on advertising, sales increase by 1.19 dollars. C. For every additional 1 dollor spent on advertising, sales increase by 28.69 dollars. D. For every additional 1 dollor spent on advertising, sales decreases by 28.69 dollars. E. For every additional 1 dollor spent on advertising, sales increase by 27.5 dollars.
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergent (R). The marketing director collects 36 weekly observations on S, A and R to estimate the following multiple regression equation: S = a + bA + cR .where, S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10% level or better.DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON FOBSERVATIONS: 36 0.2247 4.781 0.0150VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTIMATE ERRORINTERCEPT 175086.0 63821.0 2.74 0.0098A 0.8550 0.3250…
Given are five observations for two variables, x and y. xi 3 12 6 20 14 yi 55 45 50 15 20 #1) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. y= #2) Use the estimated regression equation to predict the value of y when x = 13.
The below data on the production volume x and total cost y (in dollars) for a particular manufacturing operation were used to develop the estimated regression equation y = 1,217.33 + 7.68x. Production Volume Total Cost ($) $ (units) 400 Submit Answer 450 550 600 700 750 4,100 4,900 5,400 5,900 6,500 (a) The company's production schedule shows that 650 units must be produced next month. What is the point estimate of the total cost (in dollars) for next month? (Round your answer to the nearest cent.) $6209.33 7,000 (b) Develop a 99% prediction interval for the total cost (in dollars) for next month. (Round your answers to the nearest cent.) X to $ X (c) If an accounting cost report at the end of next month shows that the actual production cost during the month was $6,700, should managers be concerned about incurring such a high total cost for the month? Discuss. Since $6,700 is within the prediction interval, managers should not be concerned about Incurring such a high total cost for one…
(a) For United States, provide data for the variables below over the years 1993 –2007:(i) Net migration rate (per 1,000 population)(ii) Total fertility rate (live births per woman)(iii)Unemployment, general level (Thousands)(iv) Wages(v) Life expectancy at birth for both sexes combined (years)Data can be obtained from the UN database http://data.un.org/Explorer.aspxUsing R-Studio, estimate a regression equation to determine the effect of unemployment,general level, wages and life expectancy at birth for both sexes on the net migration rate.(All codes and regression output should be provided).(i) Write down the regression equation. (ii) Interpret the coefficients and determine which of the individual coefficients in theregression model are statistically significant. In responding, construct and test anyappropriate hypothesis. (iii) Interpret the coefficient of determination.
Consider the following linear regression model that relates income per capita in thousand dollars of a country i (GDP P Ci), with its percentage of the population in the agricultural sector (P Ai): Model : GDP P Ci = β0 + β1P Ai + ui (a) Explain in words how to interpret parameters β0 and β1. What sign do you think these parameters might have? Explain. (b) Draw the (population) regression line associated with this model assuming that parameters β0 and β1 have the sign you have indicated in answering question (2a). Explain the meaning of this regression line.
a) For United States, provide data for the variables below over the years 1993 – 2007: (i) Net migration rate (per 1,000 population) (ii) Total fertility rate (live births per woman) (iii)Unemployment, general level (Thousands) (iv) Wages (v) Life expectancy at birth for both sexes combined (years) Data can be obtained from the UN database http://data.un.org/Explorer.aspx Using R-Studio, estimate a regression equation to determine the effect of unemployment, general level, wages and life expectancy at birth for both sexes on the net migration rate. (All codes and regression output should be provided).(i) Write down the regression equation. (ii) Interpret the coefficients and determine which of the individual coefficients in theregression model are statistically significant. In responding, construct and test anyappropriate hypothesis. (iii) Interpret the coefficient of determination. (iv) Using the 10% level of significance, determine and discuss whether the overallregression equation…
(a) For United States, provide data for the variables below over the years 1993 – 2007: (i) Net migration rate (per 1,000 population) (ii) Total fertility rate (live births per woman) (iii)Unemployment, general level (Thousands) (iv) Wages (v) Life expectancy at birth for both sexes combined (years) Data can be obtained from the UN database http://data.un.org/Explorer.aspx Using R-Studio, estimate a regression equation to determine the effect of unemployment, general level, wages and life expectancy at birth for both sexes on the net migration rate. (All codes and regression output should be provided).(b) Using R-Studio redo the regression analysis with the total fertility rate as an additionalindependent variable. (All codes and regression output should be provided).(i) Write down the regression equation. (ii) Use the 5% level of significance, determine and discuss whether the total fertilityrate has a significant impact on the net migration rate in your assigned country.…
(a) For United States, provide data for the variables below over the years 1993 – 2007: (i) Net migration rate (per 1,000 population) (ii) Total fertility rate (live births per woman) (iii)Unemployment, general level (Thousands) (iv) Wages (v) Life expectancy at birth for both sexes combined (years) Data can be obtained from the UN database http://data.un.org/Explorer.aspx Using R-Studio, estimate a regression equation to determine the effect of unemployment, general level, wages and life expectancy at birth for both sexes on the net migration rate. (All codes and regression output should be provided). (iv) Using the 10% level of significance, determine and discuss whether the overall regression equation is statistically significant. In responding, construct and test any appropriate hypothesis. (v) Determine and interpret the confidence interval for the independent variable(s).
Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 9 18 8 25 21 (b) Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 13.
29. Below is some of the regression output from a regression of the amount rental houses on an island rent for (expressed in thousands of $'s) based on the size of the house (expressed in square feet), whether the house has an ocean front view (VIEW = 1 if it has an ocean front view and = 0 if not), and an interaction term between the ocean front view dummy variable and the size of the house. If the estimated equation isPrice = 1,444 + 0.3*Size + 1,411*View + 0.08*(Size*View) How much more (or less) does a 3800 square foot house that has an ocean front view rent for compared to a similar sized house without an ocean front view? (if the ocean front house rents for more then express your answer as a POSITIVE number; if the ocean front house rents for less then express your answer as a NEGATIVE number) (please express your answer using 1 decimal places)