My id number – 00006885 Question 1

Question 3.

a)



is multiple leaner regression.

and

In this case, t_crit is 2.052 (df is 27, α is 0.05)

While this result is higher than t_crit that means we reject H₀

b)

The partial correlation coefficient is obtained because X2 and Y need a correlation coefficient that does not affect X3. It can also be defined as:

r_{1 3.2} = PCC among Y and X₃, since X₂ constant

r_{1 2.3} = PCC among Y and X₂, since X₃ constant

r_{2 3.1} = PCC among X₂ and X₃, since Y constant

Question 4.

a)

Plotting NGDP and RGDP as liner graph against time

b)

RGDP = 1907.715 + 128.782 * year

R squared =99.14%

SE of variable =1.966646

SE of const=1907.715

NGDP=-986.3317+201.9772*Year

R squared=92.77%

Standard Error of variable =9.267489

Standard Error of Const=212.6816

c)

B2 in RGDP shows that annual GDP growth averaged 128,782. However, the average annual growth rate of B2 in nominal GDP is 201.9772

d)

Real GDP is adjusted for inflation, and due to measurements produced at constant prices, the B2 level is only 128,782, indicating higher results due to the increase in nominal GDP product prices. In addition, nominal GDP is not adjusted to the inflation rate. But, government agencies mostly turn to real GDP because it is a more reliable economic indicator.

e)

You can use the GDP deflator to determine the average inflation rate in the selected years of this model, which can be considered as an economic indicator that converts real GDP to nominal:

GDP deflator=NGDP/RGDP*100% and GDP deflator=201.9772/128.782*100%= 156.83

Question 5.

a)

According to this regression model presented above, R-square = 0.6968, which determines the high value and 69.68%, explains all the variability of the response value relative to the mean value. To find the R-square manually, we need to utilize the regression model ESS, RSS, and TSS. Standard error (SE) = 2324.9; ESS = Residue = 264 850 533; RSS = Model = 608 559 605 and TSS = Total = 873 410 138 for the source.

Calculating R- squared.

R- squared= RSS/TSS= 608,559,605/873,410,138 = 0.6968 = 69.68%

According to TSS=ESS+RSS = 264,850,533 + 608,559,605 = 873,410,138

b)

Knowing the 95% confidence interval for B2, we should to determine the consumption coefficient (B₂) and this B₂ standard error. As a result, the 95% confidence interval for the slope in the sample. Our estimation: B₂ = 3.3076, and the calculated standard error is 0.31172. We have 51 - 2 = 49 df. From the T-table, we determine that t₄₉,_0.05 = 1.664.

2.6776 ≤ β₂ ≤ 3.9376

As a result, H₀ is fail to reject in this 3.0 slope coefficient

c)

spending is equal $5,000

Salary_i = 12,129.52+ 3.3076*Spend_i + u<sub>i

plug in</sub> Salary_i = $12,129.52 + $3.3076*$5,000 = $28,667.52 we found this.

standart error is 2324.9 (determined by SE = √SSE / (nk-1)), the 95 percent confidence interval for actual and average wages with this SE is as follows: ($ 23,920; $ 33,365) , which amounts to 28 667.52 US dollars, ± (2021) * (2324.9).

d)



To check Residuals normality.

Checking Jarque- Bera test

In this regression model, they are the most frequently compared choice to test for normality and correlation between all endogenous and exogenous factors. In many cases, the Jarque-Bera test is a worthy test because the sample data has a limited and redundant value compared to conventional printing. Formerly known as Carlos Jarque and Anil K. Bera. Test measurements are not consistently negative. If it is far from zero, it does not indicate normal data transmission and is used to determine how much information is reflected in the environment using a routine task and to calculate the probability of arbitrary changes on a regular basis. data were distributed. We can know that both variables are interrelated and how they are assigned on a regular basis, which is different from the level of alpha (a) in both simple tests. Based on the Jarque-Bera test, checking p-values ​​is always a smart idea. For example, a small p-score and a large quadratic stimulus from this test mean that you can reject the erroneous theory that information is usually given. In our iteration model, 95% confidence, between a = 0.05 and P-score = 0,000, and this means that we can reject H0. In addition, using the Jark-Bera test, chi-square = 2.56 and P-value = 0,000, this means that a high chi-square score and a low P-value mean that this information is typically assigned and H₀ is rejected

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