Question

4. The following data set presents CPI (Consumer Price Index) of the US and the price of a regular cheese pizza at the same time. CPI 30.2 48.3 12.3 162.2 191.9 197.8 Cost of Pizza 0.15 0.35 1.00 1.25 1.75 2.00 (a) (10 points) Assuming a linear relation between CPI (a) and pizza price ), find the least square estimation for the regression coefficients. (b) (10 points) Use the data to test the hypothesis that the pizza price does not depend on the CPL Use the 5 percent level of significance.
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Answer #1

Following is the output of regression analysis generated by excel:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.985221899 0.970662189 0.963327737 0.141459647 6 ANOVA df MS Significance F Regression Residual Total 2.648290007 2.648290007 132.34282540.000325975 0.080043327 0.020010832 2.728333333 4 5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept CPI (x) 0.161601497 0.122662576 -1.317447437 0.258083335 -0.5021674070.178964413 0.000874247 11.50403518 0.000325975 0.007630071 0.01248467 0.01005737

(a)

The least square regression line is

y' = -0.1616 +0.0101x

(b)

Here we can check either correlation coefficient, or slope or we can use F test statistics.

Using slope:

Hypotheses are:

Но : 31-0

H_{a}:eta_{1} eq 0

From output, test statistics is

t = 11.504

The p-value is 0.0003

Since p-value is less than 0.05 so we reject the null hypothesis. That is we cannot conclude that the pizza price does not depend on the CPI.

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