PLEASE help with Question 4 I only need help with question 4, as questions 1,2,

Question

PLEASE help with Question 4
I only need help with question 4, as questions 1,2, and 3 have already been answered and will be provided for reference if you need them
thanks in advance

I only need help with question 4

HERE ARE THE ANSWERS FOR PREVIOUS QUESTIONS

1.

2.

3.

The quarterly sales data (number of book sold) for Christian book over the past three years in California follow: You must use Excel to compute the time series (regression) equation Yearl 1690 940 2625 2500 Year2 1800 900 2900 2360 Year3 1850 1100 2930 2615 uarter 4 a time series plot. What type of pattern exists in the data? or 2. Use the following dum any seasonal effects in the data Quarter 1-0; Quarter 2=1 if the 3-1 if the sales data riables to develop an esti rl=1 gression equation to account for es data point is in Quarter 1, otherwise is in Quarter 2, otherwise, Quarter 2-0; Quarter r 3, otherwise er 3-0. the quarterly forecasts for next year 4. Let t-1 to refer to the observation in quarter 1 of year ; t-2 to refer to the observation in quarter 2 of year lim,and t=12 to refer to the observation in quarter 4 of year 3, Using the dummy variables defined in part (b) and t, develop an estimated regression equation to account for seasonable effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the guarterlv forecasts for next year Based on the result, what factors might lead to the highest Christian book sales in quarter 3?

Explanation / Answer

By using the dummy variable for seasonal trend:

Using Minitab:

Regression Analysis: Sold versus t, Q1, Q2, Q3

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 4 6065392 1516348 187.92 0.000
t 1 68450 68450 8.48 0.023
Q1 1 559770 559770 69.37 0.000
Q2 1 3076938 3076938 381.33 0.000
Q3 1 181405 181405 22.48 0.002
Error 7 56483 8069
Total 11 6121875

Model Summary

S R-sq R-sq(adj) R-sq(pred)
89.8279 99.08% 98.55% 97.44%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 2306.7 82.0 28.13 0.000
t 23.12 7.94 2.91 0.023 1.12
Q1 -642.3 77.1 -8.33 0.000 1.66
Q2 -1465.4 75.0 -19.53 0.000 1.57
Q3 349.8 73.8 4.74 0.002 1.52

Regression Equation

Sold = 2306.7 + 23.12 t - 642.3 Q1 - 1465.4 Q2 + 349.8 Q3

Forecasting for next year:

t: Q1=13, Q2=14, Q3=15 and Q4=16

Prediction for Sold

Regression Equation

Sold = 2306.7 + 23.12 t - 642.3 Q1 - 1465.4 Q2 + 349.8 Q3

t=13 and Q1=1, Q2=0,Q3=0

Sold= 2306.7+23.12*13 -642.3*1 - 1465.4*0+349.8*0

Sold= 1964.96

Variable Setting
t 13
Q1 1
Q2 0
Q3 0

Fit SE Fit 95% CI 95% PI
1965 82.0013 (1771.10, 2158.90) (1677.40, 2252.60)

Variable Setting
t 14
Q1 0
Q2 1
Q3 0

Fit SE Fit 95% CI 95% PI
1165 82.0013 (971.098, 1358.90) (877.397, 1452.60)

Variable Setting
t 15
Q1 0
Q2 0
Q3 1

Fit SE Fit 95% CI 95% PI
3003.33 82.0013 (2809.43, 3197.24) (2715.73, 3290.94)

Variable Setting
t 16
Q1 0
Q2 0
Q3 0

Fit SE Fit 95% CI 95% PI
2676.67 82.0013 (2482.76, 2870.57) (2389.06, 2964.27)

Seasonal factor has more effect on Christian book sales and one unit of Q3 adding 349.8 more book sales.

Quarter t Sold Q1 Q2 Q3 1 1 1690 1 0 0 2 2 940 0 1 0 3 3 2625 0 0 1 4 4 2500 0 0 0 1 5 1800 1 0 0 2 6 900 0 1 0 3 7 2900 0 0 1 4 8 2360 0 0 0 1 9 1850 1 0 0 2 10 1100 0 1 0 3 11 2930 0 0 1 4 12 2615 0 0 0

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