Does the evidence suggest a linear relationship between the happiness index and life expectancy? Explain. b) If appropriate, predict the happiness index value for a country with a life expectancy of 75.
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6. An economist studies the relationship between a
happiness index (y) and life expectancy (x) for
individual countries. Assume the SLR model.
We know: n = 26, Y-hat = 0.98 + 0.08x , and
the 95% CI: 0.05 < β1 < 0.11.
a) Does the evidence suggest a linear
relationship between the happiness index
and life expectancy? Explain.
b) If appropriate, predict the happiness index
value for a country with a life expectancy of 75.
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- Assume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?on the basis of the value of linear correlation coefficient, would you conclude, at the /r/>0.9 level, that the data can be reasonably modeled linear equation?A large policy debate revolves about the causes and consequences of child labour. Extensive child labour at early ages is often considered as harmful and there is substantial theoretical and empirical interest in determining the causes for child labour. Therefore, we would like to analyze the relationship between wealth (e.g. the number of cattle or other assets) and child labour, using household data collected in several villages in rural Africa. Suppose we have data on Y and X iv where Y, is the number of hours worked by child i in village v and X, is family wealth. a) Explain how this is related to the concept of Panel Data. b) Explain how you could estimate the relationship between wealth and child labour using pooled OLS, Random Effect (RE), Fixed Effect (FE) estimators. Write down the estimation equations and the conditions needed to guarantee consistency. Compare the FE and the OLS estimators: Is either of these two estimators based on weaker assumptions than the other? c)…
- 8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?A survey of high school students was done to examine whether students had ever driven a car after consuming a substantial amount of alcohol (1=yes, 0=no). Data was collected on their sex (male/female), race (White/non-White), and grade level (9,10,11,12). Researchers realized that the impact of race on consuming alcohol before driving might vary by grade level and decided to fit the following model. Variable Coding = 1 if Intercept Sex () Female Race () Black Grade level ( 9th grade 10th grade 11th grade [Reference = 12th grade] Attached is the logistic model 1. Compute the OR of drinking before driving for students who self-reported as Black versus non-Black in the 9th grade, adjusting for gender. 2. Compute the OR of drinking before driving for students who self-reported as Black versus non-Black in the 12th grade, adjusting for gender. 3. Compute the OR of drinking before driving for someone in the 9th grade versus 12th grade for a student who…
- 9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5Suppose a researcher believes that the occurrence of natural disasters such as earthquakes leads to increased activity in the construction industry. he decides to collect province-level data on employment in the construction industry of an earthquake-prone country, like Japan, and regress this variable on an indicator variable that equals 1 if an earthquake took place in that province in the last five years. a. Should the researcher include province fixed effects in order to control for location specific characteristics of the labor market? b. What can the researcher to control for the location effects?24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.
- A study was conducted to assess the impact of nutrient enrichment on zooplankton densities in A & B Islands. An ecologist sampled populations of zooplankton in these two locations and observed the nutrient enrichment level was higher in A island when compared with the level in B island. It is predicted the zooplankton densities in A island will be greater than those found in B island.A multiple linear regression model based on a sample of 13 weeks is developed to predict standby hours based on the total staff present and remote hours. The SSR is 23,638.17 and the SSE is 33,273.99. a. Determine whether there is a significant relationship between standby hours and the two independent variables (total staff present and remote hours) at the 0.05 level of significance. What are the correct hypotheses to test?1. Which data set has an apparent negative, but not perfect linear relationship between its two variables? 2. In which data set is there evidence of a strong nonlinear relationship between its two variables? 3. Which data set indicates the strongest negative linear relationship between its two variables? 4. Which data set indicates a perfect positive linear relationship between its two variables?
