In an experiment to determine the factors affecting tensile strength in steel plates, the tensilestrength (in kg/mm?), the manganese content (in parts per thousand), and the thickness (inmm) were measured for a sample of 20 plates. The following MINITAB output presents theresults of fitting the model Tensile strength = Bo + B1 Manganese + B2 Thickness.The regression equation isStrength = 26.641 + 3.3201 Manganese – 0.4249 ThicknessPredictorCoef StDevт РConstant26.6412.723409.78 0.000Manganese 3.32010.3319810.00 0.000Thickness -0.42490.12606 -3.37 0.004S = 0.8228 R-Sq = 86.2% R-Sq(adj) =84.6%Analysis of VarianceSS MS2 72.0136.005 53.190.000SourceDFRegressionResidual Error 1711.508 0.6769Total1983.517Predict the strength for a specimen that is 10 mm thick and contains 8.2 ppta.manganese.b. If two specimens have the same thickness, and one contains 10 ppt more manganese,by how much would you predict their strengths to differ?If two specimens have the same proportion of manganese, and one is 5 mm thickerthan the other, by how much would you predict their strengths to differ?C.

Answered: In an experiment to determine the…

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?
Suppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…
According to World Health Organization (WHO), the recommended limit for a noise level inside a classroom is 35 dBA. However, nine out of ten schools fail to meet this recommendation. A researcher wishes to conduct a study relevant to the prior information, but as a gap, he decides to include the area (in square meters) of every classroom and how it could possibly affect the resulting noise level. He selects 17 classrooms at random, and the noise levels are recorded in the next slide. a. Find the regression equation and construct the scatter plot diagram. b. Predict the noise level if a classroom has an area of 85.97 m2 . c. Calculate the coefficient of determination and interpret the findings. d. Calculate the coefficient of alienation and interpret the findings. Use Excel
A multiple linear regression model based on a sample of 13 weeks is developed to predict standby hours based on the total staff present and remote hours. The SSR is 23,638.17 and the SSE is 33,273.99. a. Determine whether there is a significant relationship between standby hours and the two independent variables (total staff present and remote hours) at the 0.05 level of significance. What are the correct hypotheses to test?
The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals). b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals). c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents (Y). Analysis on the set finds that the regression equation is Y=60-0.5*X. What can be said of the correspondence (relation) between age and accidents? Are younger workers safer or more prone to accident? What is the likely number of accidents for someone aged 25?
The Mayor of texas whom is partners with a local agriculturalist wants to know how the amount of fertilizer and the amount of water given to plants affect their growth. The results were inputted into MINITAB so as to fit the model a) Write out the regression equation b) What is the sample size used in this investigation? c) Determine the values of *, ** and ***, **** d) Conduct a hypothesis test, at the 5% level of significance, to determine whether ? is significant. e) What would be the growth of the plant if 4g of fertilizer and 7g of ater was given to it daily? f) Carry out an F -test at the 1% significance level to determine whether the model is significant
The systolic blood pressure dataset (in the third sheet of the spreadsheet linked above) contains the systolic blood pressure and age of 30 randomly selected patients in a medical facility. What is the equation for the least square regression line where the independent or predictor variable is age and the dependent or response variable is systolic blood pressure? Y=__________ X + ______________ Patient 7 is 67 years old and has a systolic blood pressure of 170 mm Hg. What is the residual? __________ mm Hg Is the actual value above, below, or on the line? What is the interpretation of the residual? (difference in actual &predicated bp, difference in age, the amount of systolic changes)
In a study of possible correlation between the height in cm (X) and the weight in kg (Y) of chimpanzees, a sample of 40 animals produces a correlation coefficient of r=0.813 and a regression line with equation Y=0.34X+19.5. What is the expected weight of a chimpanzee that is 157 cm tall? Round off final answer to 2 decimal places.
A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3% Analysis of VarianceSource DF SS MS F pRegression 3 1991.31…
A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15 Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15a) What is dependent and independent variables? [2]b) Fully write out the regression equation [1] c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’ [4] d) Hence test whether ? is significant. Give reasons for your answer. [4]…

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