Question

Could you teach me do this by Ti83or 84？

Below is data collected over 6 specific years. The data collected is the Consumer Price Index (CPT) and the cost of a slice of pizza We would like to build a model using the CPI to predict the cost of a slice of pizza in a given year. Year 1960 1973 1986 1995 2002 2003 CPI (x) 30.2 48.3 112.3 162.2 191.9 197.8 Cost of a slice 0.15 0.35 1.00 1.25 1.75 2.00 of pizza () 1.) Plot the data. Are we justified in creating a Linear Regression model to predict the price of a pizza slice using the CPI? Why or why not? 2.) Calculate the descriptive statistics. 3.) Calculate the sums of squares 4.) Calculate the slope, intercept and the correlation. What is this correlation value telling us? 5.) Assemble the prediction equation, and interpret the slope within the context of the problem. 6.) State the hypotheses for the hypothesis test for regression 7.) Fill in the ANOVA table below. Source df MS p-value Regression Error Total 8) What's your decision at a 5% significance level? Why? 9) State your conclusion. Do we have evidence of a relation between X and Y? Why or why not? 10.) Calculate the coefficient of determination (P). What does this tell us? 11.) In the year 2000, the CPI was 187.1. Predict the cost of a slice of pizza that year. Provide a prediction interval. Don't forget to make a concluding statement in the context of the problem. 12 ) Notice that the margin of error in the prediction interval is fairly high (about 25% of the point estimate) Why is this? What could we do to make our prediction more accurate?

Answer 1

i have done it through data pack(excel add-inns). It might help you understand the results.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.985222
R Square	0.970662
Adjusted R Square	0.963328
Standard Error	0.14146
Observations	6

ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.64829	2.64829	132.3428	0.000326
Residual	4	0.080043	0.020011
Total	5	2.728333

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.1616	0.122663	-1.31745	0.258083	-0.50217	0.178964	-0.50217	0.178964
x	0.010057	0.000874	11.50404	0.000326	0.00763	0.012485	0.00763	0.012485

RESIDUAL OUTPUT				PROBABILITY OUTPUT
Observation	Predicted y	Residuals		Percentile	y
1	0.142131	0.007869		8.333333	0.15
2	0.324169	0.025831		25	0.35
3	0.967841	0.032159		41.66667	1
4	1.469704	-0.2197		58.33333	1.25
5	1.768408	-0.01841		75	1.75
6	1.827746	0.172254		91.66667	2

ro^ability Plot series Sample Percentile

H0: X AND Y ARE INDEPENDENT(no relation b/w cpi and pizza price)

H1: AT LEAST ONE PAIR OF VALUES DEPENDS ON EACH OTHER(relation exist)

Since F CAL> F TAB, We reject the null hyp.

that is,there exist a relationship b/w cpi and pizza price.

now

r2 tells the percentage of variability explained by the regression model. From the above results it seems that almost 97% of the variability in Y is explained by X.

We can make our predictions more accurate by introducing more independent variables that have linear relationship with response variable to the model(but not too many or the model will become complex). Also, we can include more observation for having more info incorporated to the mode