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a) In the manufacturing of plastic material, it is believed that the cooling time (in seconds) has an influence on the plastic material impact strength (in kJ/m²). Therefore, a study is carried out in which plastic material impact strength is determined for nine different cooling times. The results of this experiment are shown in the following table: Cooling Times 10 15 20 25 Impact Strenth 48.6 42.1 36.2 31.8 28.7 27.4 25.5 21.2 20.8 30 35 40 45 50 3 UTM UTM i. Fit a linear regression model relating the impact strength to cooling times. UTM UTMUTr ii. Test at a = 0.05 level of significance whether there exists a negative linear relationship between the impact strength and cooling times. UTM B UTM UTM b) In a certain chemical process, the reaction time is related to the temperature in the chamber in which the reaction takes place. The reaction time (minutes) and the temperature (°C) is observed. Assume that the reaction time and temperature are normally distributed. The results from a randomly selected sample are shown in a Microsoft Office Excel output as follows: UTM UT SUMMARY OUTPUT Regression Statistics Multiple R UTM 0.973111 R Square Adjusted R Square UTM 0.946946 Standard Error 0.941641 UTMUTM UTM Observations 8.002571 12UTM UTM Coefficient TMUTM Intercept Std Error Reaction Time 112.9708625 t-Stat p-value 20.4465 1.73x10-9 -13.3599 1.06x10-7 5.525194167 -1.788111888 0.133841721 i. Is there any significant relationship between the reaction time and tem- UTM perature? Use a = 0.05 level of significance. ii. State the value that is often used to check the adequacy of a regression UTM model. UTM UTM TM iii. Fit a linear regression model relating reaction time to temperature.

a) In the manufacturing of plastic material, it is believed that the cooling time (in seconds) has an influence on the plastic material impact strength (in kJ/m²). Therefore, a study is carried out in which plastic material impact strength is determined for nine different cooling times. The results of this experiment are shown in the following table: Cooling Times 10 15 20 25 Impact Strenth 48.6 42.1 36.2 31.8 28.7 27.4 25.5 21.2 20.8 30 35 40 45 50 3 UTM UTM i. Fit a linear regression model relating the impact strength to cooling times. UTM UTMUTr ii. Test at a = 0.05 level of significance whether there exists a negative linear relationship between the impact strength and cooling times. UTM B UTM UTM b) In a certain chemical process, the reaction time is related to the temperature in the chamber in which the reaction takes place. The reaction time (minutes) and the temperature (°C) is observed. Assume that the reaction time and temperature are normally distributed. The results from a randomly selected sample are shown in a Microsoft Office Excel output as follows: UTM UT SUMMARY OUTPUT Regression Statistics Multiple R UTM 0.973111 R Square Adjusted R Square UTM 0.946946 Standard Error 0.941641 UTMUTM UTM Observations 8.002571 12UTM UTM Coefficient TMUTM Intercept Std Error Reaction Time 112.9708625 t-Stat p-value 20.4465 1.73x10-9 -13.3599 1.06x10-7 5.525194167 -1.788111888 0.133841721 i. Is there any significant relationship between the reaction time and tem- UTM perature? Use a = 0.05 level of significance. ii. State the value that is often used to check the adequacy of a regression UTM model. UTM UTM TM iii. Fit a linear regression model relating reaction time to temperature.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
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Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...
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QUESTION 3 a) In the manufacturing of plastic material, it is believed that the cooling time (in UT seconds) has an influence on the plastic material impact strength (in kJ/m²). UTM Therefore, a study is carried out in which plastic material impact strength is UTM determined for nine different cooling times. The results of this experiment are shown in the following table: UTM Cooling Times 10 Impact Strenth 48.6 15 yUT 50 21.2 20.8 20 25 TM 42.1 30 35 31.8 28.7 27.4 25.5 36.2 40 45 3 UTM UTM i. Fit a linear regression model relating the impact strength to cooling times. sUTM UTM ii. Test at a = 0.05 level of significance whether there exists a negative linear relationship between the impact strength and cooling times. UTMU UT UTM b) In a certain chemical process, the reaction time is related to the temperature in the chamber in which the reaction takes place. The reaction time (minutes) and the temperature (°C) is observed. Assume that the reaction time and temperature are normally distributed. The results from a randomly selected UTM SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square UTM UN UTM UT 0.973111 UTM 0.946946 Standard Error 0.941641 Observations UTM UTM UTM 8.002571 12 UTM UT TMUTM t-Stat UTM Intercept Coefficient Std Error Reaction Time 112.9708625 P-value U 20.4465 1.73×10-9 i. Is there any significant relationship between the reaction time and tem- -1.788111888 5.525194167 0.133841721 UTM -13.3599 1.06x10-7 perature? Use a = 0.05 level of significance. UTM UT UTM ii. State the value that is often used to check the adequacy of a regression model. UTM UTM UTM iii. Fit a linear regression model relating reaction time to temperature. UTM UTM UTM UTM U UTM UTM UT UTM UTM
Transcribed Image Text:QUESTION 3 a) In the manufacturing of plastic material, it is believed that the cooling time (in UT seconds) has an influence on the plastic material impact strength (in kJ/m²). UTM Therefore, a study is carried out in which plastic material impact strength is UTM determined for nine different cooling times. The results of this experiment are shown in the following table: UTM Cooling Times 10 Impact Strenth 48.6 15 yUT 50 21.2 20.8 20 25 TM 42.1 30 35 31.8 28.7 27.4 25.5 36.2 40 45 3 UTM UTM i. Fit a linear regression model relating the impact strength to cooling times. sUTM UTM ii. Test at a = 0.05 level of significance whether there exists a negative linear relationship between the impact strength and cooling times. UTMU UT UTM b) In a certain chemical process, the reaction time is related to the temperature in the chamber in which the reaction takes place. The reaction time (minutes) and the temperature (°C) is observed. Assume that the reaction time and temperature are normally distributed. The results from a randomly selected UTM SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square UTM UN UTM UT 0.973111 UTM 0.946946 Standard Error 0.941641 Observations UTM UTM UTM 8.002571 12 UTM UT TMUTM t-Stat UTM Intercept Coefficient Std Error Reaction Time 112.9708625 P-value U 20.4465 1.73×10-9 i. Is there any significant relationship between the reaction time and tem- -1.788111888 5.525194167 0.133841721 UTM -13.3599 1.06x10-7 perature? Use a = 0.05 level of significance. UTM UT UTM ii. State the value that is often used to check the adequacy of a regression model. UTM UTM UTM iii. Fit a linear regression model relating reaction time to temperature. UTM UTM UTM UTM U UTM UTM UT UTM UTM
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