Question

Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time is needed for the joint to set (measured in hours) as it is related to temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R² = 0.827 to answer the following questions.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.914	0.765	10.3445	2.7E-06	6.183	9.644
Temp(F)	-0.083	0.013	-6.565	0.000103	-0.112	-0.055

Find the residual for a temperature of 60 F, if the time to set was 2.41 hours.

Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time is needed for the joint to set (measured in hours) as it is related to temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R² = 0.827 to answer the following questions.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.914	0.765	10.3445	2.7E-06	6.183	9.644
Temp(F)	-0.083	0.013	-6.565	0.000103	-0.112	-0.055

Which is the correct interpretation of the sample slope in the context?

	1.	For each increase of 1 degree of temperature in F, the time needed to joint set decreases 0.083 hours on average.
	2.	For each increase of 1 degree of temperature in F, the time needed to joint set decreases 7.914 hours on average.
	3.	For each increase of 1 degree of temperature in F, the time needed to joint set increases 7.914 hours on average.
	4.	For each increase of 1 degree of temperature in F, the time needed to joint set increases 0.083 hours on average.

Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time is needed for the joint to set (measured in hours) as it is related to temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R² = 0.827 to answer the following questions.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.914	0.765	10.3445	2.7E-06	6.183	9.644
Temp(F)	-0.083	0.013	-6.565	0.000103	-0.112	-0.055

Which is the correct interpretation the coefficient of determination in context?

	1.	82.7% of the sample variance in time is explained by the regression with temperature.
	2.	90.9% of the sample variance in time is explained by the regression with temperature.
	3.	82.7% of the sample variance in temperature is explained by the regression with time.
	4.	90.9% of the sample variance in temperature is explained by the regression with time.

Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time is needed for the joint to set (measured in hours) as it is related to temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R² = 0.827 to answer the following questions.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.914	0.765	10.3445	2.7E-06	6.183	9.644
Temp(F)	-0.083	0.013	-6.565	0.000103	-0.112	-0.055

Which of the following is the correct interpretation of the correlation coefficient in context?

	1.	There is a strong positive linear relationship between time and temperature.
	2.	There is a moderate negative linear relationship between time and temperature.
	3.	There is a moderate positive linear relationship between time and temperature.
	4.	There is a strong negative linear relationship between time and temperature.

Answer 1

Solution

1)Find the residual for a temperature of 60 F, if the time to set was 2.41 hours.

so the actual value of temperature of 60 F, if the time to set was 2.41 hours

Now find the predicting the amount of time is needed for the joint to set when temperature is 60 F.

So we have regression equation

amount of time =7.914-0.083*Temp(F)

amount of time =7.914-0.083*60

amount of time = 2.93

Residual = Actual value - predicted value

Residual = 2.41 - 2.93 = -0.52

2)Which is the correct interpretation of the sample slope in the context?

For each increase of 1 degree of temperature in F, the time needed to joint set decreases 0.083 hours

3)

Which is the correct interpretation the coefficient of determination in context?

82.7% of the sample variance in time is explained by the regression with temperature.

4)Which of the following is the correct interpretation of the correlation coefficient in context?

4.	There is a strong negative linear relationship between time and temperature.