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.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8377ed26-f203-475d-87e2-79ea4c92cbec%2Fd2c952b9-4730-439f-ab27-944f7186943d%2F7y5gt_processed.jpeg&w=3840&q=75)
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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