Linear regression and hypothetis testing

ebayissues

hello all,


I am preparing for my January exams on quants and I'm just trying to get to speed with linear regression and hypothesis testing.


So I did a sample regression here question here, its not 100% right so I would like to know were I have done something wrong.


Samuel hinges has for a number of years built and updated models that explain and predict the French presidential election. The basic premise is that the share of the vote secured by the party in power at the time of the election is affected by a number of macroeconomic factors such as the growth rate and the inflation rate in the economy at the time of the election. To test this consider running the following regression

The Excel results when this regression is run using data from 1880 to 2000 are reported below
Vote = B1 + B2(growth) + B3(inflation)+e

(i)Interpreting the results, The multiple regression model has the equation Y^ = B1 + B2(x) + B3(x)+ e

Starting off with the co-efficient
The X variable (inflation) is negative meaning that there’s a negative relationship between inflation(x) variable and the vote our Y variable or the dependent variable.
So in inflation goes up by a certain amount the number of votes will fall.
On the next independent variable which is growth rate it has a positive relation with votes meaning that if the growth rate increase there will be an increase in the share of Votes being won.
Mathematically putting this equation with the assumption that both variables go up by 4 and 5 respectively, vote is 52.44357 + 0.648761( 4) – 0.16622(5%). Here your vote rate is = 54.21
Another question is that is the regression a good fit? Meaning do the X VARIABLES explain Y very well. To do so we look at the adjusted R2 which is adjusted for the number of different X variables. The adjusted R2 is 0.329667 so almost 39% of the X variables explain Y, this number is very low.
Take a look at the individual co- efficient if they are statistically significant. Could growth rate and inflation be zero, meaning it has no effect of votes.
We can do this test by talking a look at the P- Value, using a 95% confidence interval a P value of less than .05% is good looking at growth it has a number of 0.00056 so it should be in our model.

(ii)
Suppose the inflation rate is 4% and the growth rate is -4%. On the basis of the above results predict the winner of an election in these circumstances

Vote is 52.44357 + 0.648761(4) – 0.16622(5%). Here your vote rate is = 54.37. This is not yet complete, but I am not sure where to move on from here.

hivizman

You are broadly on the right lines, and I think that you can be a little more precise in how you interpret the regression statistics.

You can first of all check whether the coefficients are significant, that is, what is the probability of obtaining a coefficient equal to or greater than (in absolute value) the coefficient in the regression from a random sample of observations, if the true coefficient in the underlying population is zero (that is, the "true" constant is zero or the independent variable in question does not affect the dependent variable). This is done by calculating a t-statistic, and then determining the probability associated with this t-statistic and assessing this against a significance criterion such as p<0.05. You have stated p for the growth variable, but you should also do this for the constant and the inflation variable.

Assuming that all coefficients are significant, the regression can be interpreted as follows: assuming that growth and inflation are both zero, then we would predict that the incumbent party would receive 52.44357% of the vote in a presidential election (the incumbent's expectation to get more than half of the vote is a common effect sometimes called the "incumbency advantage"). For every additional percentage point added to the growth rate, the incumbent party would expect an additional 0.648761% of the vote, while for every additional percentage point added to the inflation rate, we would expect the incumbent party's share of the vote to fall by 0.16622%. Hence extra growth is "good news" for the incumbent and extra inflation is "bad news". The R-squared figure of 0.329667 means that variation in the growth rate and inflation rate explain around 33% of the variation in the incumbent's share of the vote, leaving 67% to be explained by variation in other potential independent variables. For many economists, this would actually be considered quite good, in that we have a "parsimonious" model (two independent variables) that explains about one-third of the variation in our dependent variable. There are certainly omitted variables, but are we missing anything that would have a big impact on the incumbent's share of votes?

In part (ii), remember that a negative growth rate will be "bad news" and will tend to reduce the incumbent party's share of the votes. Inflation will also be "bad news". So you would expect the incumbent party's share to be less than the "base" 52% share implied by the constant.