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 49 consumer items.

	Basket of Goods 1
	Coefficients	Standard Error	t Stat	P-value
Intercept	4.529	0.280	16.186	0
Basket of Goods1	0.202	0.023	8.585	0

	Basket of Goods 2
	Coefficients	Standard Error	t Stat	P-value
Intercept	4.206	0.773	5.443	0.000
Basket of Goods2	0.255	0.068	3.730	0.001

	Basket of Goods 3
	Coefficients	Standard Error	t Stat	P-value
Intercept	6.511	0.192	33.892	0.000
Basket of Goods3	0.053	0.018	2.944	0.005

	Regression Statistics
	Basket of Goods 1	Basket of Goods 2	Basket of Goods 3
Multiple R	**	0.478	0.395
R square	0.611	0.228	0.156
Adjusted R Square	0.602	0.212	0.138
Standard Error	0.316	0.419	0.449
Observations	49	49	49

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.

(1 mark) The correlation between CPI and Basket of Goods 1 is: (Answer) (3dp - remember to include a negative sign if appropriate)

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

(1 marks) Which variable is a better 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.

(2 marks) Why? Choose the most appropriate answers to justify your answer to Question 2 above.

A: 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 & D

H: Both B & E

I: Both C & F

J: There is not enough information to make a decision.