Question

Develop a simple linear regression model to predict the Cost of Living Index based upon Restaurant Price Index using a 95% level of confidence.

1. Write the reqression equation.
2. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.
3. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4. Interpret the coefficient for the independent variable.
5. What percentage of the observed variation in income is explained by the model?
6. Predict the value of the cost of living index using this regression model with a Restaurant Price Index of 110.00

Create a table and compare the preceding three simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

Data from Excel File

City	Cost of Living Index	Rent Index	Groceries Index	Restaurant Price Index	Local Purchasing Power Index
Luanda, Angola	150.82	138.03	171.77	121.3	50.27
Basel, Switzerland	145.92	62.61	139.31	134.41	144.12
Lausanne, Switzerland	140.88	57.61	144.89	117.3	165.05
Perth, Australia	138.97	72.08	126.03	131.02	112.02
Bern, Switzerland	136.3	57.31	133.11	124.59	158
Sydney, Australia	135.92	93.61	125.27	113.28	116.18

Answer 1

a)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.271149
R Square	0.073522
Adjusted R Square	-0.1581
Standard Error	6.299925
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	12.59825	12.59825	0.317424	0.603245
Residual	4	158.7562	39.68906
Total	5	171.3545
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	117.0995	43.32936	2.702543	0.053952	-3.20214	237.4011
Restaurant Price Index	0.197079	0.349802	0.563404	0.603245	-0.77413	1.168284

y^ = 117.0995 + 0.1971 x

b)

F = 0.3174

p-value = 0.6032

since p-value > alpha

we fail to reject the null hypothesis

the model is not significant

c)

p-value of independent variable is also same 0.6032

since p-value > alpha

we fail to reject the null hypothesis

we conclude that the independent variable is not significant

d)

when restaurant price index increase by 1, on average cost of living index increase by 0.1971

e)

R^2 = 0.0735

hence 7.35 %

f)

x = 110

y^ = 117.0995 + 0.1971 *110

= 138.7805