Homework Help: Regression formula (calculating trends)

1. Jul 5, 2014

Hi guys,

I have been tasked with the following question;

The company has set a fixed budget for Period 1 of the financial year using the following figures as being 100% of the budget:

Material costs £200 000
Labour costs £100 000

£38 000 / £16 000 and £14 000 respectively, whilst the Fixed overheads had an adverse variance of £2 000.

a) Set out the fixed budget using the budgeted figures above, and calculate the actual figures, the variances and the trends.

Ok, so taking material costs as an example, I have to calculate the actual figures of the fixed budget (this is given as £200k).

Calculate the variance, this is a positive variance of £38k, therefore material cost was actually £200K-£38K=£162K.

Now, in calculating the trend.having done a bit of statistics in the past and am familiar with the regression formula, in which I would calculate the slope and the y intercept and insert the data into the formula;

y=a+bx

But in this instance that seems a bit long winded, am I overcomplicating this, or is it just a case of opening excel and getting on with it using the regression equation.

Regards

Joe
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 5, 2014

Ray Vickson

Are you sure you have interpreted the data/question correctly? How can you possibly estimate a trend (i.e., time-behaviour) without having several data points spread out over different time periods?

Are you sure that "favourable variance", etc, is not speaking about time-behavour? That is, are you sure that material cost in period 2 will not be 200,000 - 38,000 (that is, 38,000 better next period)? If this is not what is meant I cannot make any sense of the problem's statement; I know quite a bit about Statistics, but have never heard the term "favourable variance", etc. Variance is just variance, favourable or not. If you have seen some other meanings in your course material you need to explain it here, because your terminology is non-standard.

3. Jul 5, 2014

As for course material, I have absolutely none, not even a link to a website. It is a level 5 module, so I suppose that I am expected to just get on and research, however I have a lot of family life getting in the way at them moment and cant afford it as much time as I would like.

Item Budget Actual Variance Favourable/ Adverse? Difference (%) Trend
Material costs £200,000 £162,000 £38,000 Favourable 19% y=232000-32000(x)
Labour costs £100,000 £84,000 £16,000 Favourable 16% y=116000-16000(x)
Variable overheads £50,000 £36,000 £14,000 Favourable 28% y=64000-14000(x)
Total £400,000 £334,000 £66,000 Favourable 16.50% y=64000-14000(x)

This is what I have cobbled together... whether it is correct or not is a different matter!!!

In terms of calculating the trend I used the standard linear regression equation...
a=(∑y-b(∑x) ))/n

b=(n∑xy-(∑x)(∑y))/(n∑x^2-(∑x)^2)

4. Jul 5, 2014