The Central England Temperature data consist of temperatures recorded in Central

Question

The Central England Temperature data consist of temperatures recorded in Central England from 1659–2005. It is the longest instrumental record of temperature in the world. The measurements are average values from several recording stations within a triangle in Central England (roughly between London, Manchester and Bristol).
Data for the month of January from 1659 to 2005 is shown in the following plot.
(a) Which of the following features does this plot most clearly display? Trend Seasonality Trend and Seasonality Autocorrelation
(b) What differencing would you apply to this data? Second Order Seasonal differencing of order 6 Seasonal differencing of order 12 None of the above
A linear model was applied to this data and the following output was obtained: > model <- lm(temperatures ~ years) > summary(model) Call: lm(formula = temperatures ~ years)
Residuals: Min 1Q Median 3Q Max -6.145 -1.148 0.192 1.355 4.251
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -5.28798 1.90781 -2.77 0.0059 ** years 0.00464 0.00104 4.46 0.000011 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.94 on 345 degrees of freedom Multiple R-squared: 0.0546, Adjusted R-squared: 0.0519 F-statistic: 19.9 on 1 and 345 DF, p-value: 0.0000109 (c) What does the model estimate the average temperature in January has changed by every century? Enter your answer to 3 decimal places (a) Which of the following features does this plot most clearly display? Trend Seasonality Trend and Seasonality Autocorrelation
(b) What differencing would you apply to this data? Second Order Seasonal differencing of order 6 Seasonal differencing of order 12 None of the above
A linear model was applied to this data and the following output was obtained: > model <- lm(temperatures ~ years) > summary(model) Call: lm(formula = temperatures ~ years)
Residuals: Min 1Q Median 3Q Max -6.145 -1.148 0.192 1.355 4.251
Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -5.28798 1.90781 -2.77 0.0059 ** years 0.00464 0.00104 4.46 0.000011 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.94 on 345 degrees of freedom Multiple R-squared: 0.0546, Adjusted R-squared: 0.0519 F-statistic: 19.9 on 1 and 345 DF, p-value: 0.0000109 (c) What does the model estimate the average temperature in January has changed by every century? Enter your answer to 3 decimal places (d) Is this estimated change statistically significant? Yes No Output is inclusive Unable to say based on the output
(e) Given that the mean and the corrected sum of squares for all the years modelled are ar{x}=1832 and S(x,x) = 3481798 respectievely, what does the model estimate the average temperature in January was in the year 2000? Answer the question with a 95% confidence interval to 3 decimal places. Lower bound:Answer Upper bound: Answer (f) If an autocorrelation plot of the residuals of this fitted model was to be produced, where should horizontal lines marking a 95% confidence band be placed? Enter your answers to 3 decimal places. Lower bound: Answer Upper bound: Answer (d) Is this estimated change statistically significant? Yes No Output is inclusive Unable to say based on the output
(e) Given that the mean and the corrected sum of squares for all the years modelled are ar{x}=1832 and S(x,x) = 3481798 respectievely, what does the model estimate the average temperature in January was in the year 2000? Answer the question with a 95% confidence interval to 3 decimal places. Lower bound:Answer Upper bound: Answer (f) If an autocorrelation plot of the residuals of this fitted model was to be produced, where should horizontal lines marking a 95% confidence band be placed? Enter your answers to 3 decimal places. Lower bound: Answer Upper bound: Answer
January 1650 1700 1750 800 1850 1900 1950 2000

Explanation / Answer

a) The plot clearly displays SEASONALITY, since the plot shows variations within a year.

b) We should apply SEASONAL DIFFERENCING OF ORDER 12 since the variations are based on 12 months.

c)The estimate of average temperature in January that has changed by every century is 0.005.

d) YES it is statistically significant since it's p-value is very small.

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