Transcript Regression Problem 1 t246 Ft  16.86  0.5t At182022 What is your forecast fore the next period? In which period are we? 7. Next period is.

Regression Problem 1
t
1
2
3
4
5
6
7
Ft  16.86  0.5t
At
19
18
15
20
18
22
20
What is your forecast fore the next period?
In which period are we?
7.
Next period is 8.
F8  16.86  0.5(8)  20.86
SUMMARY OUTPUT
Standard Deviation of Forecast = 2.09
Regression Statistics
Multiple R
0.492518281
R Square
0.242574257
Adjusted R Square
0.091089109
Standard Error
2.090796157
Observations
7
Forecast using simple regression
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
SS
1
5
6
MS
F
7
7
21.85714286 4.371428571
28.85714286
Coefficients Standard Error
t Stat
16.85714286
1.767045268 9.539734585
0.5
0.395123334 1.265427671
Significance F
1.60130719
0.261481287
P-value
0.000214193
0.261481287
Lower 95%
Upper 95%
12.31480839 21.39947732
-0.515696865 1.515696865
Regression Problem 2
Given the following regression report for the relationship between
demand and time. (Demand is the dependent variable and Time is
the independent variable)
SUMMARY OUTPUT
What is your forecast for
the next period?
52+10(20+1) = 262
What is the standard
deviation of your forecast
for the next period? 15.05
Regression Statistics
Multiple R
0.97
R Square
0.95
Adjusted R Square
0.95
Standard Error
15.06
Observations
20
ANOVA
Regression
Residual
Total
df
1
18
19
Intercept
X Variable 1
Coefficients
52
10
SS
75988
4083
80071
Standard Error
7.00
0.58
MS
75988
227
t Stat
7.44
18.30
F
335
P-value
6.80516E-07
4.42292E-13
Significance F
4.42292E-13
Lower 95%
37.34
9.46
Upper 95%
66.73
11.92
Is there a strong relationship between the dependent and the
independent variables?
Yes R-Square (Coefficient of Determination) id 0.95, Multiple R
(Correlation Coefficient) is 0.97, p-value is very small
Is the relationship positive or negative?
Positive. We can check it by Multiple R being + or b1 being +
Short Questions 1-2
1. If the coefficient of determination between interest rate (x) and
residential real estate prices (y) is 0.85, this means that:
A) 85% of the y values are positive
B) 85% of the variation in y can be explained by the variation
in x
C) 85% of the x values are equal
D) 85% of the variation in x can be explained by the variation
in y
E) none of the above
2. Which value of the coefficient of correlation (r) indicates a
stronger correlation than 0.7?
A) 0.6
B) -0.9
C) 0.4
D) -0.5
E) none of the above
Short Questions 3-4
3. In a good regression we expect
A) P-value to be high and R-square to be high
B) P-value to be low and R-square to be low
C) P-value to be low and R-square to be high
D) P-value to be high and R-square to be low
E) none of the answers
4. Discuss the relationship between MAD in moving average and
exponential smoothing and Standard Error in regression.
Standard Error in regression is an estimate of the Standard
Deviation of the Forecast.
Standard Deviation of the Forecast = Standard Error
MAD in moving average and exponential smoothing is an
estimate of the Standard Deviation of the Forecast.
Standard Deviation of the Forecast = 1.25MAD