Question

DATAfile: CorporateBonds

Company Ticker	Years	Yield
GE	1	0.767
MS	1	1.816
WFC	1.25	0.797
TOTAL	1.75	1.378
TOTAL	3.25	1.748
GS	3.75	3.558
MS	4	4.413
JPM	4.25	2.31
C	4.75	3.332
RABOBK	4.75	2.805
TOTAL	5	2.069
MS	5	4.739
AXP	5	2.181
MTNA	5	4.366
BAC	5	3.699
VOD	5	1.855
SHBASS	5	2.861
AIG	5	3.452
HCN	7	4.184
MS	9.25	5.798
GS	9.25	5.365
GE	9.5	3.778
GS	9.75	5.367
C	9.75	4.414
BAC	9.75	4.949
RABOBK	9.75	4.203
WFC	10	3.682
TOTAL	10	3.27
MTNA	10	6.046
LNC	10	4.163
FCX	10	4.03
NEM	10	3.866
PAA	10.25	3.856
HSBC	12	4.079
GS	25.5	6.913
C	25.75	8.204
GE	26	5.13
GE	26.75	5.138
T	28.5	4.93
BAC	29.75	5.903

A statistical program is recommended.

A sample containing years to maturity and yield (%) for 40 corporate bonds is contained in the data file named CorporateBonds.†

(a) Develop a scatter diagram of the data using x = years to maturity as the independent variable.

Does a simple linear regression model appear to be appropriate?

Given the upward trend of the data on the left side of the plot, a linear regression model would predict higher values for the data on the right side of the plot. So, a curvilinear regression model appears to be more appropriate.Since the data on the left and right sides of the plot both trend downward at about the same rate, a linear model is appropriate.    Given the downward trend of the data on the left side of the plot, a linear regression model would predict lower values for the data on the right side of the plot. So, a curvilinear regression model appears to be more appropriate.Since the data on the left and right sides of the plot both trend upward at about the same rate, a linear model is appropriate.

(b) Develop an estimated regression equation with x = years to maturity and x² as the independent variables. (Round your numerical values to two decimal places.)

ŷ =

Answer 1

Regression Analysis
	R²	0.668
	Adjusted R²	0.650
	R	0.817
	Std. Error	0.958
	n	40
	k	2
	Dep. Var.	Yield,y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	68.3011	2	34.1506	37.19	1.40E-09
Residual	33.9750	37	0.9182
Total	102.2761	39
Regression output				confidence interval
variables	coefficients	std. error	t (df=37)	p-value	95% lower	95% upper
Intercept	1.02
Years,x	0.46	0.0814	5.662	1.80E-06	0.2958	0.6255
x^2	-0.01	0.0026	-3.964	.0003	-0.0155	-0.0050

a)Given the upward trend of the data on the left side of the plot, a linear regression model would predict higher values for the data on the right side of the plot. So, a curvilinear regression model appears to be more appropriate

b)

ŷ = 1.02+0.46*x-0.01*x²