Modeling Lowe's Sales - Simonoff(1)

7/24/2019 Modeling Lowe's Sales - Simonoff(1)

1/12

Modeling Lowes sales

Forecasting sales is obviously of crucial importance to businesses. Revenue streams are

random, of course, but in some industries general economic factors would be expected to have

a great effect on sales. One such industry is the building supply industry, since contractor

work is a driving force for such purchases.

Is it possible to model sales of Lowes Companies (the worlds second largest home im-

provement retailer and the 14th largest retailer in the U.S.) as a function of generally available

economic factors related to the housing industry? The data studied here were gathered by

Mike Nannizzi, and refer to 79 consecutive quarters from the first quarter of 1983 through

the third quarter of 2002. We are interested in modeling Lowes quarterly sales, in millions of

dollars, as a function of housing starts (in millions) and average mortgage rate (I also thank

Mike for some of the financial analysis quoted here). Examination of the revenue variable

shows that it is righttailed; since it is a money variable, it is natural to take the targetvariable as logged (base 10) sales. That is, we will fit a semilog model.

Recall, by the way, that these sales are in millions of dollars, so these quarterly sales are as

big as $7.5 billion. Theres a lot of money in hammers and nails!

Here are scatter plots of logged sales versus housing starts and mortgage rate. As wouldbe expected, there is a direct relationship with housing starts (more new houses meaning

more building supplies), and an inverse relationship with mortgage rate (higher rates meaning

fewer purchases of houses, with the resultant fewer repairs). We also see evidence in both

plots of two distinct subgroups in the data, with apparently different relationships between

the variables. The group with flatter sales corresponds to the 1980s, while that with higher

sales corresponds to the 1990s.

c2015, Jeffrey S. Simonoff 1


2/12

There is also a strong relationship between logged sales and time, reflecting an annual

proportional growth in sales. Once again we see evidence that the 1980s and 1990s correspond

to two distinct time periods. Why would that be? Unlike Home Depot, which was the market

leader in the (urban and suburban) home improvement industry, Lowes spent the 1980s in

mostly rural markets, aiming to support local contractors. As the home improvement concept

became tremendously profitable into the 1990s, Lowes changed its focus to compete more

directly with Home Depot.



3/12

Here are the results of fitting the model of logged revenue on the three predictors:

Regression Analysis: Log Sales versus Housing starts, Mortgage, Time

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Regression 3 11.8100 3.93665 4924.32 0.000

Housing starts 1 0.3727 0.37271 466.23 0.000

Mortgage 1 0.0138 0.01377 17.23 0.000Time 1 2.4666 2.46663 3085.49 0.000

Error 75 0.0600 0.00080

Total 78 11.8699

Model Summary

S R-sq R-sq(adj) R-sq(pred)

0.0282742 99.49% 99.47% 99.44%

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 1.8700 0.0444 42.16 0.000

Housing starts 0.09847 0.00456 21.59 0.000 1.13

Mortgage 0.01551 0.00374 4.15 0.000 5.67

Time 0.018073 0.000325 55.55 0.000 5.44



4/12

Regression Equation

Log Sales = 1.8700 + 0.09847 Housing starts + 0.01551 Mortgage + 0.018073 Time

The regression fit is apparently very strong. The coefficients can be interpreted as follows.

An increase of one million housing starts in a quarter is associated with increasing sales by

25.5%, holding all else fixed (10.0985 = 1.255). The coefficient for mortgage rates is puzzling,

as it is positive; an increase in mortgage rate by one percentage point is associated with

an increase in sales of 3.6% (10.01551 = 1.036), holding all else fixed. In fact, this variable

adds little to the fit, as the model with it removed has R2 = .994. Finally, given the other

variables, there is a 4.2% quarterly increase in sales (10.01807 = 1.042).

Unfortunately, there are problems with this model. There is apparently structure left in

the data, related to the time effect noted earlier. In addition, there is a strong effect that

sales in the third quarter are systematically lower than during the rest of the year.



5/12

We can try to address these model deficiencies by adding two more predictors: Time2,

to address the parabolic pattern in the residuals related to time, and an indicator variable

identifying the third quarter. Here is the resultant regression output:



Regression 5 11.8416 2.36831 6100.00 0.000

Housing starts 1 0.2340 0.23395 602.58 0.000Mortgage 1 0.0010 0.00103 2.66 0.107

Time 1 0.1370 0.13696 352.77 0.000

Time sq 1 0.0103 0.01035 26.65 0.000

Q3 1 0.0168 0.01681 43.29 0.000

Error 73 0.0283 0.00039

Total 78 11.8699

Model Summary

S R-sq R-sq(adj) R-sq(pred)0.0197040 99.76% 99.74% 99.71%

Coefficients


Constant 2.0649 0.0489 42.27 0.000



6/12

Housing starts 0.09386 0.00382 24.55 0.000 1.64

Mortgage 0.00517 0.00317 1.63 0.107 8.43

Time 0.014280 0.000760 18.78 0.000 61.17

Time sq 0.000037 0.000007 5.16 0.000 37.43

Q3 -0.03489 0.00530 -6.58 0.000 1.08

Regression Equation

Log Sales = 2.0649 + 0.09386 Housing starts + 0.00517 Mortgage + 0.014280 Time

+ 0.000037 Timesq - 0.03489 Q3

The collinearity between Time and Time2 is to be expected, so we dont have to worry

about that. Apparently we dont need mortgage rate now, so that original positive coefficient

wasnt something to worry about anyway:



Regression 4 11.8405 2.96013 7457.39 0.000

Housing starts 1 0.2329 0.23293 586.82 0.000

Time 1 0.2886 0.28855 726.94 0.000

Time sq 1 0.0214 0.02136 53.82 0.000

Q3 1 0.0165 0.01650 41.56 0.000Error 74 0.0294 0.00040

Total 78 11.8699

Model Summary


0.0199233 99.75% 99.74% 99.71%

Coefficients


Constant 2.1379 0.0197 108.65 0.000

Housing starts 0.09349 0.00386 24.22 0.000 1.63

Time 0.013331 0.000494 26.96 0.000 25.30

Time sq 0.000044 0.000006 7.34 0.000 25.25

Q3 -0.03453 0.00536 -6.45 0.000 1.08



7/12

Regression Equation

Log Sales = 2.1379 + 0.09349 Housing starts + 0.013331 Time + 0.000044 Time sq

- 0.03453 Q3

Given time, and whether it is the third quarter, one million additional housing starts is

associated with an expected 24.0% increase in Lowes sales. Given time and the number of

housing starts, sales are 7.7% lower in the third quarter. Why would this be? We wouldnt

be surprised to see higher sales in the first part of the year, since that is the peak construction

season in the northern part of the country, but why wouldnt this affect the fourth quarter

as well? In fact, there is evidence that Lowes sold goods at a steeper discount in the fourth

quarter, as its income as a percentage of sales is onethird lower than in any of the otherthree quarters. This could, perhaps, reflect a desire to pump up endofyear sales, so as to

meet analysts sales expectations.

The time effect is a little trickier, since it is a quadratic relationship. Since the coefficient

for Time2 is positive, were seeing an increasing growth rate in sales over time, and a little

calculus can make that more specific. Given all else is held fixed, the expected rate of change

of the response as a function of a predictorxwhenxis in the model quadratically (1x+2x2)

is just the partial derivative with respect to x, or 1+ 22x. Thus, given all else is held

fixed, at the first quarter of 1983 the estimated expected time-related rate of sales growth is

3.1% (.0133314 + (2)(.00004389)(1) =.0134, and 10.0134 = 1.031); on the other hand, given

all else is fixed, at the first quarter of 2002 the estimated expected time-related rate of sales

growth is 4.7% (.0133314 + (2)(.00004389)(77) = .0201, and 10.0201 = 1.047). Thus, unless

economic conditions change, it seems that Lowes sales can be expected to continue to rise.

The model now seems to fit pretty well (although the plots of residuals versus housing

starts and time of year seem to hint at nonconstant variance).



8/12



9/12

Given the very highR2, we can say that housing starts and the timerelated variables, we

can predict Lowes sales very accurately. Indeed, the standard error of the estimate s= .0199

implies that 95% of the time Lowes sales are predicted to within roughly 910% high or low

(10.0398 =.912; 10.0398 = 1.096). Of course, that translates into as much as $750 million,

so we shouldnt get too excited!

Another potential approach we could have taken here is to split the data into pre1990

and post1990 groups, being consistent with the earlier scatter plots. We can do this using

the pooled / constant shift / full model approach we discussed earlier. Here is the full model

fit:



Regression 9 11.8515 1.31683 4923.18 0.000

Housing starts 1 0.0889 0.08893 332.48 0.000

Time 1 1.2738 1.27379 4762.25 0.000

Mortgage 1 0.0059 0.00586 21.90 0.000

Q3 1 0.0155 0.01555 58.12 0.000

1980s 1 0.0086 0.00864 32.29 0.000

Housing80s 1 0.0001 0.00007 0.25 0.619

Time80s 1 0.0138 0.01385 51.77 0.000

Mortgage80s 1 0.0052 0.00523 19.56 0.000

Q380s 1 0.0031 0.00313 11.70 0.001

Error 69 0.0185 0.00027

Total 78 11.8699



10/12

Model Summary


0.0163547 99.84% 99.82% 99.79%

Coefficients


Constant 1.8473 0.0394 46.88 0.000

Housing starts 0.08892 0.00488 18.23 0.000 3.87

Time 0.019151 0.000278 69.01 0.000 11.83

Mortgage 0.01631 0.00349 4.68 0.000 14.77

Q3 -0.04195 0.00550 -7.62 0.000 1.69

1980s 0.4004 0.0705 5.68 0.000 329.84Housing80s -0.00356 0.00714 -0.50 0.619 60.92

Time80s -0.005737 0.000797 -7.20 0.000 12.17

Mortgage80s -0.02239 0.00506 -4.42 0.000 233.21

Q380s 0.03226 0.00943 3.42 0.001 2.12

Regression Equation

Log Sales = 1.8473 + 0.08892 Housing starts + 0.019151 Time + 0.01631 Mortgage

- 0.04195 Q3 + 0.4004 1980s - 0.00356 Housing80s - 0.005737 Time80s

- 0.02239 Mortgage80s + 0.03226 Q380s

Separate slopes for the housing starts variable dont seem to be supported:



Regression 8 11.8514 1.48142 5598.58 0.000

Housing starts 1 0.1606 0.16057 606.82 0.000

Time 1 1.5004 1.50040 5670.29 0.000

Mortgage 1 0.0059 0.00586 22.16 0.000

Q3 1 0.0158 0.01578 59.63 0.000

1980s 1 0.0095 0.00950 35.92 0.000

Time80s 1 0.0138 0.01380 52.14 0.000

Mortgage80s 1 0.0052 0.00518 19.58 0.000

Q380s 1 0.0031 0.00314 11.85 0.001

Error 70 0.0185 0.00026



11/12

Total 78 11.8699

Model Summary

S R-sq R-sq(adj) R-sq(pred)0.0162667 99.84% 99.83% 99.80%

Coefficients


Constant 1.8501 0.0388 47.72 0.000

Housing starts 0.08726 0.00354 24.63 0.000 2.07

Time 0.019204 0.000255 75.30 0.000 10.10

Mortgage 0.01632 0.00347 4.71 0.000 14.76Q3 -0.04140 0.00536 -7.72 0.000 1.62

1980s 0.3866 0.0645 5.99 0.000 279.51

Time80s -0.005695 0.000789 -7.22 0.000 12.04

Mortgage80s -0.02224 0.00503 -4.42 0.000 232.37

Q380s 0.03088 0.00897 3.44 0.001 1.94

Regression Equation

Log Sales = 1.8501 + 0.08726 Housing starts + 0.019204 Time + 0.01632 Mortgage

- 0.04140 Q3 + 0.3866 1980s - 0.005695 Time80s- 0.02224 Mortgage80s + 0.03088 Q380s

This model implies predictions of sales to within 78%, roughly 95% of the time. The

model yields two fitted lines: for the 1980s,

LogSales= 2.2368+.0873Housing starts+.01351Time.0059Mortgage rate.0105Q3,

and for post1990,

LogSales= 1.8501+.0873Housing starts+.0192Time+.0163Mortgage rate.0414Q3.

The housing starts effect is very similar to that in the quadratic model, and the third

quarter effect was stronger in the later time period. Consistent with the increasing predic-



12/12

tions from the quadratic model, the estimated annual rate of change in sales (given the other

variables) was 3.2% in the earlier time period, and 4.5% in the latter time period, certainly

good news for Lowes. Interestingly, a similar analysis to this one using Home Depot revenues

shows the opposite pattern, with the rate of change of Home Depots revenues decreasing

in recent time periods. Perhaps this accounts for the relatively poor performance of HomeDepot stock; Home Depots price dropped more than 50% from June 2002 to March 2003,

while that of Lowes dropped only (?) 15%.

There are two other points worth mentioning here. These data form a time series, of

course, and even though the plot of standardized residuals versus time didnt show apparent

autocorrelation, there is, in fact, some autocorrelation in the residuals. Its not that impor-

tant, however; some basic time series remedies (which we will talk about later) only change

the standard error of the estimate from .0163 to .016. In addition, we should recognize that

part of the time trend effect that we are seeing is presumably an inflation effect; an analysis

that avoided that (uninteresting) effect could be accomplished by using constant dollar sales

(inflation-adjusted), rather than the actual (nominal) dollar sales.

Minitab commands

To create all Kindicators for a categorical variable (like Quarter) click onCalc Make

Indicator Variables and enter the variable name under Indicator variables for:.

The program will choose default names for the indicators, but you can change them ifyou wish.


Modeling Lowe's Sales - Simonoff(1)

Documents

Transcript of Modeling Lowe's Sales - Simonoff(1)