With inflation and the impact of higher prices on households' cost of living under the spotlight, the Office for National Statistics(ONS) announced changes to the 2022 basket of goods to reflect people's inflation experiences in the UK, in line with the current circumstances.

Below are three regression outputs fitting the consumer prices index (CPI) to a different basket of goods, each basket of goods consists of 52 consumer items.

	Regression Statistics
	Basket of Goods 1	Basket of Goods 2	Basket of Goods 3
Multiple R	0.773	0.39	0.577
R square	0.598	0.152	0.333
Adjusted R Square	0.59	0.135	0.319
Standard Error	0.289	0.511	0.395
Observations	52	52	52

	Basket of Goods 1
	Coefficients	Standard Error	t Stat	P-value
Intercept	4.548	0.289	15.758	0
Basket of Goods1	**	0.026	8.619	0

	Basket of Goods 2
	Coefficients	Standard Error	t Stat	P-value
Intercept	4.92	0.663	7.42	0
Basket of Goods2	0.198	0.066	**	0.004

	Basket of Goods 3
	Coefficients	Standard Error	t Stat	P-value
Intercept	6.159	0.198	31.074	0
Basket of Goods3	0.08	0.016	4.994	**

Assume that assumptions for simple linear regression are satisfied. Use the above tables to answer the following questions, either choose the most correct option, or type in the answer to the number of decimal places specified.

(2 mark) What is the value of the regression slope between CPI and Basket of Goods 1? Answer

1. (3dp - remember to include a negative sign if appropriate) with the degrees of freedom equals to Answer(integer)

(1 mark) What is the absolute value of the test statistic for CPI and Basket of Goods 2? Answer

1. (3dp)

(2 mark) Is there a significant linear relationship between CPI and Basket of Goods 3 AnswerYesNo

The economists are interested in which basket of goods most accurately predicts CPI. Use the regression results to answer the following questions.

1. (1 marks) Which variable is a better predictor of CPI? AnswerA: Basket of Goods 1.B: Basket of Goods 2.C: Basket of Goods 3.D: None of them is a good predictor of CPI.

A: Basket of Goods 1.

B: Basket of Goods 2.

C: Basket of Goods 3.

D: None of them is a good predictor of CPI.

1. (2 marks) Why? Choose the most appropriate answers to justify your answer to Question 4 above. AnswerA: Correlation between CPI and Basket of Goods 1 is the highest.B: Correlation between CPI and Basket of Goods 2 is the highest.C: Correlation between CPI and Basket of Goods 3 is the highest.D: The slope of regression equation for the linear relationship between CPI and Basket of Goods 1 was significantly different than zero.E: The slope of regression equation for the linear relationship between CPI and Basket of Goods 2 was significantly different than zero.F: The slope of regression equation for the linear relationship between CPI and Basket of Goods 3 was significantly different than zero.G: Both A & DH: Both B & EI: Both C & FJ: There is not enough information to make a decision.

Correlation between CPI and Basket of Goods 1 is the highest.

Correlation between CPI and Basket of Goods 2 is the highest.

Correlation between CPI and Basket of Goods 3 is the highest.

The slope of regression equation for the linear relationship between CPI and Basket of Goods 1 was significantly different than zero.

The slope of regression equation for the linear relationship between CPI and Basket of Goods 2 was significantly different than zero.

The slope of regression equation for the linear relationship between CPI and Basket of Goods 3 was significantly different than zero.

Both A & D

Both B & E

Both C & F

There is not enough information to make a decision.