Stat Assignment 4

STAT160-14A – Management Statistics

Assignment 4

Simple and Multiple Regression

STEP ONE:

a) Produce a scatter plot using “Inflation” as the response (dependent) variable and “OCR” as the explanatory (independent) variable. Give a title to the plot, add axis labels and include a copy of this graph in your report.

b) Based on the scatter plot, describe the relationship between the explanatory and the response variable.

Inflation is given as the response variable and OCR is given as the explanatory variable. There is a curvilinear relationship between OCR and inflation rate. Also, although the points are spread out and are not clustered together, it can be seen visually that it still does have a positive trend. This means when OCR increases, inflation also increases, but this increase tapers off beyond certain values of OCR.

STEP TWO:

a) Fit a simple linear regression model using the Data Analysis ToolPak in Excel. Copy and paste the regression output in your report. Also, paste the residual plot and the normal probability plot.

b) Write down the regression equation you have obtained. How would you interpret the intercept and the slope in this equation?

The regression equation is given as:

Ŷi = 0.2805Xi + 0.8264 where, Ŷi = the predicted value of inflation

Xi = OCR rate

0.2805 = sample slope

0.8264 = sample Y intercept

The slope is 0.2805. This means that, for each increase of 1% in OCR, the inflation rate is estimated to increase on average by 0.28%. Thus, the slope represents the OCR rate that is estimated to vary according to the predicted inflation rate.

The Y intercept is 0.8264. The Y intercept represents the mean percentage of inflation when the OCR rate is zero. It is effectively impossible for there to be a 0% OCR rate so this Y intercept has no practical interpretation. Also, 0 is not within the range of the data so the intercept is not sensible, but only a mathematical necessity.

c)...