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A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.
ANOVA |
|
|
|
df |
SS |
Regression |
3 |
45.9634 |
Residual |
11 |
2.6218 |
Total |
|
|
|
|
|
|
Coefficients |
Standard Error |
Intercept |
0.0136 |
|
x1 |
0.7992 |
0.074 |
|
|
|
x2 |
0.2280 |
0.190 |
|
|
|
x3 |
-0.5796 |
0.920 |
|
|
A) Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
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- Analysis of Variance Source DF SS MS Regression 1 02364 13 14 Residual Error Total 11.3240 What is the value of SSR (Sums of Squares for Regression)?Regression Statistics Multiple R 0.971 R-Square A Adjusted R-Square .942 Standard Error 30.462 Observations 51 ANOVA df SS MS F Significance F Regression C 747851.57 373925.79 402.98 9.89E-31 Residual 48 D 927.91 Total 50 792391.11 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept E 62.13 26.79 1.60E-30 1539.66 1789.51 Price of Roses −6.68 F −1.41 1.64E-01 −16.16 2.81 Disposable Income (M) 9.73 0.34 G 1.23E-31 9.04 10.42…A researcher fitted following OLS regression using time series data from 1973 t0 2020 (Bar)BD =-3.7 + 0.08BD lag(t-1), -2.2LnER lag(t), + 42LnEXP lag(t)-33LnRE lag(t), +10 LnPl lag(t), R²=0.99 DW=1.4 RSS=4.5 Where BD is budget deficit as a percentage of GDP, ER, EXP, RE and Pl are Exchange rate, government expenditures, government revenues and per capita income, respectively. Ln shows natural log and "t" stands for time. i :-Interpret above results ii :- Is there any problem of Autocorrelation in above model? How do you know
- determine the regression line equation plot the line on a graph and summarize the results( reject or do not) is there enough evidence?We have estimated the impact of gross domestic product (GDP), energy consumption (ENERGY) and population (POP) on CO2 emiisions (CO2) in Cyprus. The results are as follows, Dependent Variable: CO2 Method: Least Squares Date: 04/20/17 Time: 09.46 Sample: 1990 2013 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. GDP ENERGY POP 2.002813 0.022114 -0.734352 0.203927 6.458672 0.011872 0.328388 0.293686 0,310097 1.862670 -2.236233 0.694371 0.7597 0.0773 0,0369 0.4954 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.825079 Mean dependentyar 0.798841 0.048515 Akaike info criterion 0.047074 Schwarz criterion 40.75460 Hannan-Quinn.criter. 31.44583 Durbin-Wats on stat 0.000000 3.625982 0.108170 -3.062883 -2.866541 -3.010793 1.410912 S.D. dependent yar a Write down the economie function for the above estimation by using the information obtained from above table| b- Write down the economic model for the above…A marketing analyst wants to examine the relationship between sales (in $1,000s) and advertising (in $100s) for firms in the food and beverage industry and collects monthly data for 25 firms. He estimates the modet: Sales- Bo + B1 Advertising +t. The following table shows a portion of the regression results. Coefficients Standard Error t-stat p-value Intercept 40.10 14.08 2.848 0.0052 Advertising 2.88 1.52 -1.895 0.0608 Which of the following are the competing hypotheses used to test whether the slope coefficient differs from 3? Multiple Choice Ho i bị 3; HAtbi3 Họ ib - 2.88; HAibi 2.88
- wages = B1 + B2educ + ßzexper + e where wages denotes hourly wages. We estimate the regression in R and obtain the output ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 2.0 1.0 2 0.0455 * ## educ 0.5 0.5 1 0.3173 ## exper 2.0 0.5 4 6.33e-05 *** ## --- ## Signif. codes: ****' 0. 001 '**' 0.01 **' 0.05 ' 0.1 ' ' 1 Build a 90% confidence interval for B3 using a normal approximation. (Use that if Z ~ N(0, 1) and z1-a satisfies P(Z > z1-a) = a, then zo9 = 1.28, zo95 = 1.64, Z0.975 = 1.96, zo.99 = 2.33, and z0.995 = 2.58). Oa. [2 – 1.64 x (0.5), 2 + 1.64 x (0.5)] O b. [2 – 1.28 × (0.5), 2 + 1.28 x (0.5)] c. [2 – 1.28 x (0.5)², 2 + 1.28 × (0.5)²] O d. [2 – 1.64 × (0.5)², 2 + 1.64 × (0.5)²] O e. [2 – 1.96 × (0.5)², 2 + 1.96 × (0.5)²] O f. [2 – 1.96 × (0.5), 2 + 1.96 × (0.5)]Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using Data from the Current Population Survey Dependent variable: average hourly earnings (AHE). Regressor (1) (2) (3) 5.59 5.55 College (X,) 5.57 Female (X2) -2.69 -2.67 -2.67 0.30 0.30 Age (X3) 0.70 Northeast (X4) 0.61 Midwest (Xs) -0.28 South (X) Intercept 12.94 4.49 3.83 Summary Statistics SER 6.40 6.34 6.33 0.180 0.194 0.198 0.193 ok97 0.180 4100 4100 4100 Using the regression results in column (2): On average, a worker eans $ per hour for each year that he or she ages.We know that discrimination exists. It influences wages, but also many other dimensions over the life cycle which affect wages indirectly. I run OLS regression with variables wage, age, female and degree. The dependent variable is log(wage) and we replace the variables female and degree with the interaction term. However, discrimination is not included among the observed regressors. Given that omitting confounding variables from regression model can bias the coefficient estimates, omitting discrimination would lead to biased results. Could you please help me provide an example of how unobserved gender discrimination can affect my OLS estimates. [Hint: think about ways in which discrimination can invalidate OLS assumptions.].
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