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.

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