Empirical Homework Submit

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Saint Joseph's College of Maine *

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HA 350

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Statistics

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Feb 20, 2024

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Empirical Homework Please use the dataset “salary dataset”. Explanation of each code (name of the variable) is shown below and also provided in the spreadsheet.  sx = Sex, coded 1 for female and 0 for male  rk = Rank, coded o 1 for assistant professor, o 2 for associate professor, and o 3 for full professor  yr = Number of years in current rank  dg = Highest degree, coded 1 if doctorate, 0 if masters  yd = Number of years since highest degree was earned  sl = Academic year salary, in dollars. Using the above dataset in excel, please provide answer to the following questions. Try to be as thorough as possible. You can type your answers in a word document or simply write it down by a pen or pencil. 1- Run a regression equation (model) where “academic year salary” is dependent variable and “sex” as independent variable. Explain the following in your estimation output. a) What is the value of intercept in the equation? 24696.79 b) What is the value of slope parameter for variable sex in the estimated equation? -3339.65 c) Write down the value of t-ratio for both intercept and slope parameter for sex. a. 26.33 b. -1.85 d) How do you interpret the value of estimated coefficient (slope parameter) for variable sex?

Sex and academic year salary have a negative correlation. Relative to the independent variable, the dependent variable falls. This means that for every female there will be a decrease in salary by $3339.65 Salary =24696.79+(-339.65sex) Salary Females=24696.79+(-3339.65*1)=$21357.14 Salary Males=24696.79+(-339.65*0)=$24696.79 e) Does the estimated coefficient for variable sex is statistically significant? How do you determine statistical significance? No, not statistically different P-Value .07 > Alpha .05 so fails to reject the null hypothesis; there is no relationship between the variables. The P-Value of the variable sex coefficient is compared to the alpha (significance level) of.05 for this 95% confidence interval in order to ascertain statistical significance. Since the null hypothesis in this instance is failed to reject, the P- Value of.0706 was greater than.05, making it non-statistically significant. f) What is the P-value for estimated coefficient of sex? How do you interpret that? P-Value= .0706 Alpha.05 < P-value.07 therefore not statistically significant and fail to reject the null hypothesis. There is enough data to conclude that there is a relationship between the variables of sex and academic income. g) What is the value of “coefficient of Determination” or R 2 in the estimated regression equation? R 2 = .0639 h) How do you interpret the value of R 2? With an R2 value of 0.64, sex only accounts for 6.4% of the difference in academic year income. The low correlation between the variables indicated by this value suggests that there are likely more factors influencing pay variation. i) What is the value of Residual? How do you interpret the value of residual in a regression equation? Residual Formula= actual value of y – predicted value of y

When examining a specific sample data point along a regression line, this formula is utilized. As an illustration, examining the data for Observation 1 reveals that the residual, or the gap between the actual and anticipated values of salaries, is $1653.21. The projected pay was $24696.79, but the actual compensation based on the data was $36,350. By using the formula, $11653.20 = $36,350 - $24,696.79 All residual points have a mean of 0. There is a difference in academic year wage (y) that sex (x) cannot account for. The residual, or error component, in a regression equation is this unexplained fluctuation. It is the discrepancy between y's academic year salary's actual and expected values. 2- Run a regression equation (model) where “academic year salary” is dependent variable and include sex, rank, number of year in current work, highest degree, number of year since highest degree earned as independent variable. a) Write down the estimated equation with estimated intercept and slope parameters for each independent variable. Y-hat = 11410.15 + 5586.18rk + 482.86yr – 1331.64dg – 128.79yd + 1241.79sx F(x)= a+bX+cK+dF, partial derivative of F(x) with respect to X=b b) Write down the interpretation of each estimated coefficient in word? What does it mean? Rk (positive)- as the independent variable (salary) increases, the dependent variable (rank) also increases. This means for every increase in rank, there will be a $5,586.18 increase in salary Yr (positive)- as the independent variable (salary) increases, the dependent variable (years of work) also increases. For every increase in years of work, there will be a $482.86 increase in salary. Dg (negative)- as the independent variable (degree) increases, the dependent variable (salary) decreases. For every increase in degree, there will be a $1331.64 decrease in salary. Yd (negative)- as the independent variable (the number of years since degree) increases, the dependent variable (salary) decreases. For every increase in the number of years since degree, there will be a $128.79 decrease in salary.

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Sx (positive)- as the independent variable (salary) increase, the dependent variable (sex) also increases. For every increase in sex (female), there will be a $1241.79 increase in salary. Female Salary = 11,410.15 + (1241.79*1) = $12,651.94 Male Salary = 11,410.15 + (1241.79*0) = $11,410.15 c) Which estimated coefficients are statistically significant? Which one are not statistically significant? Significant: Rank (rk), Years of work (yr) Not Significant: Degree (dg), Years since degree (yd) and sex (sx) d) What is value of R 2 for the estimated model? R 2 = 0.8547 e) How do you interpret the value of R 2 ? With an R2 value of.8547, rank, years of job, degree, years since degree, and sex account for 85.47% of the variation in academic year compensation. This greater value suggests that there may be a correlation between the variables. f) Write down the t-ratio for all estimated slope parameters. What does it mean when t-ratio has a small or big value? Rk = 8.4 Yr = 5.3 Dg = -1.3 Yd = -1.7 Combining the SEMs of the two groups yields the t ratio, which is the difference between sample means divided by the standard error of the difference. The P value is modest, and the t ratio is large (or a large negative number) if the difference is greater than the SE of the difference.

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