test_ds <- read.csv("test.csv", header = TRUE, stringsAsFactors = FALSE)
test_ds$Date <- as.Date(test_ds$Date, format=c("%Y-%m-%d"))
head(test_ds)

        Date West.Counts West.Demands  X X2.Day.West.Counts.Avg
1 2005-01-01         452        67797 NA                    NaN
2 2005-02-01         333        56151 NA                  392.5
3 2005-03-01         262        40801 NA                  297.5
4 2005-11-01         222        18694 NA                  242.0
5 2005-12-01         523        48155 NA                  372.5
6 2006-01-01         339        52230 NA                  431.0

ccf(x=test_ds$West.Counts, y=test_ds$West.Demands)

wc_ts <- ts(test_ds$West.Counts, frequency=5)
ll <- nrow(test_ds)-1
west_counts_lag <- c(NA, test_ds$West.Counts[1:ll])
dummy_seas <- factor(cycle(wc_ts))

lm_res <- lm(West.Demands ~ West.Counts + west_counts_lag + dummy_seas, data= test_ds)
summary(lm_res)



Call:
lm(formula = West.Demands ~ West.Counts + west_counts_lag + dummy_seas,
    data = test_ds)

Residuals:
   Min     1Q Median     3Q    Max
-40817  -3166    535   3322  13837

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)
(Intercept)      13437.78    7098.42   1.893 0.063175 .
West.Counts         62.57      12.31   5.084 3.88e-06 ***
west_counts_lag     41.72      12.24   3.407 0.001176 **
dummy_seas2      -3471.68    3570.92  -0.972 0.334851
dummy_seas3      -4192.77    4525.39  -0.926 0.357899
dummy_seas4     -16984.64    4601.65  -3.691 0.000484 ***
dummy_seas5      -2614.11    3886.59  -0.673 0.503785
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7349 on 60 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.8566,    Adjusted R-squared:  0.8422
F-statistic: 59.71 on 6 and 60 DF,  p-value: < 2.2e-16