Question

A building society manager wishes to investigate the degree of association between the level of
interest rates and the flow of building society deposits. The following historical data is available:

Date Interest rates Building of society deposits(inflows) £ m
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2006Jan 11 0.8
2006July 9.5 1.1
2007Jan 9 1.4
2007July 12 1.2
2008Jan 12 1.5
2008July 12 1.3
2009Jan 12.5 1.7
2009July 10 1.1
2010Jan 11 2.0
2010July 10 1.1
2011Jan 8.5 1.2
2011July 10.5 1.9
2012Jan 13 2.5
2012July 14 2.2
2013Jan 15 2.6
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Required:
Investigate the degree of association by:
(a)Calculating Pearson’s product moment correlation coefficient r;
(b)Estimating a regression line of deposits on interest rates;
(c)Calculating the coefficient of determination;
Then:
(d)Draw a scatter diagram and place your regression line on the diagram;
(e)Comment on the degree of association in the light of your findings;
(f)Predict the level of building society deposits that the manager can expect if interest rates
are:
(i)17%, or
(ii)10%
and discuss the validity of these predictions.

Answer 1

Suppose, random variables X and Y denote interest rate and deposit respectively.

(a)

Pearson’s product moment correlation coefficient is given by

Thus there is a strong positive association between interest rate and deposit.

(b)

Regression equation of y on x is given by

Here,

Number of pairs of observation

Thus value of deposit increases with increase of interest rate as well as value of deposit decreases with decrease of interest rate.

(c)

Coefficient of determination is given by

It interprets that about 50% changes of values of deposits can be explained by changes of values of interest rates.

(d)

Corresponding scatter diagram with regression line is as follows.

(e)

From the scatter diagram we observe that, on average value of deposit increases with increase of interest rate as well as value of deposit decreases with decrease of interest rate.

(f)

We first predict the values and then discuss about validity of these predictions.

(i)

For ,

(ii)

For ,

Validity of these predictions-

We observe that these values (both 17 and 10) are outside the range from which we have taken values to construct our regression equation. Hence, these predictions are not valid.