Question

(From The Consumer Price Indexes Web site) The Consumer Price Index (CPI) measures the average change over time in the prices paid by urban consumers for consumer goods and services. The CPI affects nearly all Americans because of the many ways it is used. One of its biggest uses is as a measure of inflation. By providing information about price changes in the Nation’s economy to government, business, and labor, the CPI helps them to make economic decisions. The President, Congress, and the Federal Reserve Board use the CPI’s trends to formulate monetary and fiscal policies. In the following table, x is the year and y is the CPI.

xy

1915 10.1

1926 17.7

1935 13.7

1940 14.7

1947 24.1

1952 26.5

1964 31.0  

1969 36.7

1975 49.3

1979 72.6

1980 82.4

1986 109.6

1991 130.7

1999 166.66

Answer from your excel sheet:

Write the equation in the form y= a + bx.  Round "a" to the nearest whole number, round "b" to 2 decimal places from your Excel sheet.  _____

Find the correlation coefficient from your Excel sheet. To 2 decimal places.  _____

Is it significant?  _____ (yse or no)Use http://www.socscistatistics.com/pvalues/pearsondistribution.aspx to calculate the significance with significance level 0.05.

What is the CPI for the year 1990? Use your equation in a) and round to the nearest whole number.

Answer 1

I haves used Excel , Data > Data analysis > Regression > select x, y data > ok

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8693
R Square	0.7557
Adjusted R Square	0.7353
Standard Error	25.3919
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	1	23932.90033	23932.9003	37.1196	0.0001
Residual	12	7737.004009	644.7503
Total	13	31669.90434
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-3204.93	535.292836	-5.987248827	6.33964E-05	-4371.234303	-2038.628506
x	1.66	0.2729	6.0926	0.0001	1.0681	2.2573

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Y = (-3204.93) + (1.66)X

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Correlation (r) = CORREL (x,y) = 0.87

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Yes, p-value = .000052 < 0.05

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Y = (-3204.93) + (1.66)*1990 = 98.47 = 98