Question

Regression model

Using gretl this has been estimated with the output below.

Model 1: OLS, using observations 1-57

coefficient | std. error | t-ratio | p-value | |

const | -0.6167 | 0.2360 | -2.6130 | 0.0118 |

X1 | -1.9892 | 0.0409 | -48.6760 | 0.0000 |

X2 | 0.3739 | 0.0408 | 9.1686 | 0.0000 |

X3 | 1.3447 | 0.0368 | 36.5730 | 0.0000 |

X4 | -0.4012 | 0.0320 | -12.5220 | 0.0000 |

X5 | -0.0478 | 0.1276 | -0.3746 | 0.7095 |

Mean dependent var | -6.2529 | S.D. dependent var | 4.2151 |

Sum squared resid | 6.8318 | S.E. of regression | 0.366 |

R-squared | 0.99313 | Adjusted R-squared | 0.99246 |

F(5, 51) | 1475.3 | P-value(F) | 0 |

Log-likelihood | -20.418 | Akaike criterion | 52.835 |

Schwarz criterion | 65.094 | Hannan-Quinn | 57.599 |

Construct a complete ANOVA table for this regression. Please show working

Answer #1

Given: R^{2} = 0.99313 and RSS = 6.8318

We know that,

R^{2} = 1 - (RSS/TSS)

RSS/TSS = 1 - 0.99313

RSS/TSS = 0.00687

6.8318/TSS = 0.00687

TSS = 994.4396

and TSS = ESS + RSS

ESS = TSS - RSS

ESS = 994.4396 - 6.8318

ESS = 987.6078

Degrees of freedom are calculated as:

For regression, df = k - 1 = 6 - 1 = 5

For residual, df = n - k = 57 - 6 = 51

For total, df = n - 1 = 57 - 1 = 76

Thus, the ANOVA table is:

Source | df | SS | MS | F |

Regression | 5 | 987.6078 | 197.52156 | 1474.48 |

Residual | 51 | 6.8318 | 0.13396 | |

Total | 56 | 994.4396 |

where, MS = SS/df

and F = MS_{regression}/MS_{residual}

7)
Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + β5X5i + ui
This model has been estimated by OLS. The Gretl output is
below.
Model 1: OLS, using observations 1-52
coefficient
std. error
t-ratio
p-value
const
-0.5186
0.8624
-0.6013
0.5506
X1
0.1497
0.4125
0.3630
0.7182
X2
-0.2710
0.1714
-1.5808
0.1208
X3
0.1809
0.6028
0.3001
0.7654
X4
0.4574
0.2729
1.6757
0.1006
X5
2.4438
0.1781
13.7200
0.0000
Mean dependent var
1.3617
S.D. dependent...

Q1.
Model 1: OLS, using observations 1-832
Dependent variable: VALUE
Coefficient
Std. Error
t-ratio
p-value
const
597.865
7.72837
77.36
<0.0001
***
LOT
30.8658
4.64595
6.644
<0.0001
***
Mean dependent var
610.3780
S.D. dependent var
221.7390
Sum squared resid
38795690
S.E. of regression
216.1985
R-squared
0.050492
Adjusted R-squared
0.049348
F(1, 830)
44.13736
P-value(F)
5.54e-11
Log-likelihood
−5652.552
Akaike criterion
11309.10
Schwarz criterion
11318.55
Hannan-Quinn
11312.73
2-. For the estimated regression in activity #1 above, provide
appropriate interpretations for the estimated
intercept and...

The regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + ui
has been estimated using Gretl. The output is below.
Model 1: OLS, using observations 1-50
coefficient
std. error
t-ratio
p-value
const
-0.6789
0.9808
-0.6921
0.4924
X1
0.8482
0.1972
4.3005
0.0001
X2
1.8291
0.4608
3.9696
0.0003
X3
-0.1283
0.7869
-0.1630
0.8712
X4
0.4590
0.5500
0.8345
0.4084
Mean dependent var
4.2211
S.D. dependent var
2.3778
Sum squared resid
152.79
S.E. of regression
1.8426
R-squared
0
Adjusted...

The following show the results of regression:
Housing Sold = b0 + b1 permit +b2 price + b3 employment
Dependent Variable: SOLD ,
Method: Least Squares
Date: 03/15/20 Time: 14:59
Included observations: 108
Variable Coefficient Std. Error
t-Statistic Prob.
C -61520.76 167763.0
-0.366712 0.7146
PERMIT 15.98282
.280962 12.47721 0.0000
PRICE ...

Foreign
Direct Investment and Economic Growth
Economic theory
suggests that foreign direct investment affect the economic growth
(the growth of the Gross DomesticProduct (GDP)) in developing
countries. The objective of this project is to carry out a simple
linear regression analysisto examine this theory. Your independent
and dependent variables are the growth of the foreign direct
investment andthe economic growth (the growth of the Gross Domestic
Product (GDP)) respectively.
Required Tasks:
State the regression model and determine the least
squares...

1. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this
regression using OLS and get the following results: b0=-3.13437;
SE(b0)=0.959254; b1=1.46693; SE(b1)=21.0213; R-squared=0.130357;
and SER=8.769363. Note that b0 and b1 the OLS estimate of b0 and
b1, respectively. The total number of observations is
2950.According to these results the relationship between C and Y
is:
A. no relationship
B. impossible to tell
C. positive
D. negative
2. Consider the model Ci= β0+β1 Yi+ ui. Suppose you run this...

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