Chapter 23, Problem 23.30E

a)

To determine

To construct a scatter plot.

Explanation of Solution

Given:

Scatter plot for Actual vs 3D volume construction is,

Regression Analysis
	r²	0.954	n	30
	r	0.977	k	1
	Std. Error	0.649	Dep. Var.	Actual
ANOVA table
Source	SS	df	MS	F	p-value
Regression	242.8360	1	242.8360	576.93	3.17E-20
Residual	11.7855	28	0.4209
Total	254.6214	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	0.4196	0.4671	0.898	.3767	-0.5373	1.3764
3D	2.4752	0.1031	24.019	3.17E-20	2.2641	2.6863

Therefore, least square regression equation is,

  $\widehat{y}=0.4196+2.4752x$

b)

To determine

To verify the conditions for inference.

Answer to Problem 23.30E

All the conditions satisfied.

Explanation of Solution

Given:

The scatter plot shows linearly increasing trend. Therefore, the relationship is clearly linear, the scatterplot shows no unusual pattern that would indicate not Normally distributed residuals or residuals without a constant standard deviation, and the observations are independent.

c)

To determine

To test whether the linear relationship is statistically significant.

Answer to Problem 23.30E

There is sufficient evidence to conclude that the linear relationship between two variables is statistically significant.

Explanation of Solution

Given:

Regression Analysis
	r²	0.954	n	30
	r	0.977	k	1
	Std. Error	0.649	Dep. Var.	Actual
ANOVA table
Source	SS	df	MS	F	p-value
Regression	242.8360	1	242.8360	576.93	3.17E-20
Residual	11.7855	28	0.4209
Total	254.6214	29
Regression output					confidence interval
variables	coefficients	std. error	t (df=28)	p-value	95% lower	95% upper
Intercept	0.4196	0.4671	0.898	.3767	-0.5373	1.3764
3D	2.4752	0.1031	24.019	3.17E-20	2.2641	2.6863

Null and alternative hypotheses:

  $H_0:\beta =0$

  $H_0:\beta \ne 0$

Test statistic is,

t = 24.019

P-value = 0.0000

Decision: P-value< 0.05, reject H0.

Conclusion: There is sufficient evidence to conclude that the linear relationship between two variables is statistically significant.

Therefore, 95% confidence interval for slope is,

(2.2641, 2.6863)