Please report summary results containing the estimated slope and intercept with

Question

Please report summary results containing the estimated slope and intercept with their standard errors,   number of observations, Total sum of squares (SST), Regression sum of squares (SSR), and Error sum of squares (SSE).                                                                                [3 points]         

Does the sign of the slope for the relationship between MLB player salary and years in major league you found make intuitive sense? Please interpret and explain the slope of the simple linear regression model you estimated.                                                      [4 points]

At 1% level of significance, test whether years in major league has a statistically significant effect on player salary in MLB. Please clearly show all the necessary steps and explain in words what your decision about the hypotheses means.                                  [5 points]

Please calculate and interpret the coefficient of determination (R2) for MLB player salary and years in major league in your regression result. Does the magnitude of R2 make sense for the linear regression model you estimated? Please explain.                                 [3 points]

Calculate the correlation coefficient (r) and conduct a hypothesis test involving a null hypothesis which says there is no correlation between MLB player salary and years in major league(r=0) against an alternative hypothesis which says there is correlation between the two variables ( r0). Conduct the test at 1% level of significance clearly showing all the necessary steps.                                                                                          [5 points]                                                                                                            

Use the model to predict annual salary for a player who has been playing in the major league for 8 years. If the player was actually earing 1.8 million dollars in that year what is the resulting prediction error. Why does such a prediction error arise? Please explain. [5 points]

Carefully examining the data for player salary, do you think a simple linear regression model (with its basic assumptions) was appropriate for analyzing the relationship between the two variables using these data? Please consult the slides, the text book, or any literature online to answer this question. [Hint: Construct and inspect the histogram for player salary

SUMMARY OUTPUT Regression Statistics Multiple R 0.478151672 R Square 0.228629021 Adjusted R Square 0.226431383 Standard Error 1237.804629 Observations 353 ANOVA df SS MS F Significance F Regression 1 159396721.2 1.59E+08 104.034 1.44565E-21 Residual 351 537788265 1532160 Total 352 697184986.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 248.6010592 126.1323143 1.970955 0.049514 0.530889934 496.6712284 0.53089 496.6712 years 173.4286297 17.00329945 10.1997 1.45E-21 139.987466 206.8697934 139.9875 206.8698

Explanation / Answer

· The value of the slope is 173.4286297. This value says that if there is one unit increment in part of the independent variable (x) then the dependent variable (y ) is going to be increased by 173.4286297 unit. The obtained value of the intercept is 248.6010592; this is the value of y when the value of x is zero. The value of the standard error of estimate is 1237.804629. This tells about the accuracy of the predicted value. The number of observation in this model is 353. The value of Total sum of square (SST) is 697184986.2. The value of Regression sum of squares (SSR) is 159396721.2 and the value of Error sum of squares (SSE) is 537788265.

· The sign of the slope makes a sense here as one in increasing the other is also increasing. This value says that if there is one unit increment in part of the independent variable (x) then the dependent variable (y ) is going to be increased by 173.4286297 unit.

· The p-value for t-test for the slope is approximately 0. So we reject the null hypothesis as p-value is less than .1 (level of significance). We can conclude that the major league has a statistically significant effect on player salary in MLB.

·The value of R-square is 0.2286. We can conclude that 22.86% of the player salary is going to be explained by the variable major league.

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