**Regression Analysis**

Introduction:

We choose the HP prices for the period January 2007 to august 2008, however these are daily prices that are considered, we also chose the S$P 500 index that will be used to analyze the relationship between HP prices and S$P 500 prices, the first step is to plot the data on a chart, then the description of the trends for both index and finally a __regression analysis__ to show the relationship between the two indexes.

Data:

The chart below represents the HP prices from the year 2007 to **date**,

From the above chart it is evident that the HP prices have *gradually* risen but there are troughs and peaks over time.

The chart below represents the S$P 500 prices from January 2007 to august 2008

From the above chart it is evident that there has been a gradual rise in the prices, however recently it is clear that from the year January 2008 there has been a gradual decline in the prices.

__Regression Analysis__

Regression:

We now analyze the relationship between the HP prices and the S$P index, in this section we estimate the model of the form y = a + b x where Y is the HP prices, a is a constant, b is the slope of the model and x is the S$P 500 index, using excel we plot a scatter diagram that will derive a trend line, the following summarizes the results:

From the above scatter diagram it is evident that there is a positive relationship between the variables, the result of the model is Y = 23.36 + 0.015 X, this model means that if we hold all factors constant and that the *value* of S$P 500 index is zero then the HP price will be 23.36, it is also evident that if we hold all other factors constant and increase the value of S$P 500 by one unit then HP prices will increase by 0.015 units.

Prediction:

We use the model to estimate the next month prices, we use Y = 23.36 + 0.015 X to estimate the next HP prices, we consider the value of S$P for 1st September which is 1260.31, for this reason we substitute the model as follows:

Y = 23.36 + 0.015 (1260.31)

Y = 42.26465

Therefore the predicted price for 1st September is 42.26465, from the above discussion it is evident that as S$P index rises then the HP prices will also increase.

__Regression Analysis__

Credibility of the prediction:

From the above estimation it its evident that there is a difference between the predicted value and the actual value, the other problem is that the correlation of determination value is 0.132 which means that only 13.2% of deviations in the HP prices is explained by the explanatory variable which is S$P index. The value of the correlation of determination shows that the model will not be appropriate in determining the HP prices and for this reason there is need to add more explanatory variables to the model.

References:

Yahoo finance (2008) historical prices for HP and S$P, retrieved on 2nd September, available at http://finance.yahoo.com/q?s=hpq

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