Question

y2 36 49 1760 You are a personnel director and are interested in predicting the Number of Shares of Company Stock (V) using the Number of Years Employed with the Company (X). You randomly selected 8 employees and obtain the following summary data: EmplNum NumberShares (Y) YearsEmployed (x) - XY X² 1 350 2100 122500 2 415 7 2905 172225 3 22 8 64 48400 4 520 4680 81 270400 5 355 10 3550 126025 640 8320 169 409600 7 535 14 7490196 286225 8 885 15045 289 783225 SUM 3920 84 45850 9 84 2218600 What is the Total Sums-of-Squares (SST)? (to the nearest whole number) 100 13 17

Answer 1

49 Ilme remalnlng: 01:39:52 You are a personnel director an Number of Shares of Company Stock (Y) using the Number of Years Employed with the Company (X). You randomly selected 8 employees and obtain the following summary data: EmplNum NumberShares (Y) YearsEmployed (X) XY x? 1 350 2100 36 122500 2 L 415 2905 172225 3 220 8 1760 48400 4 T 520 4680 81 270400 5 355 3550 100 126025 640 - 13 8320 169 409600 535 7490 196 286225 885 17 15045 289783225 SUM 3920 84 45850 984 2218600 What is the Total Sums-of-Squares (SST)? (to the nearest whole number) 64 10 6 14 8

Total Sum od square

$SST=\sum_{i=1}^{n}(y_{i}-\bar{y})^{2}=297800$

y	y-y_bar	(y-y_bar)2
350	-140	19600
415	-75	5625
220	-270	72900
520	30	900
355	-135	18225
640	150	22500
535	45	2025
885	395	156025
mean=490
	Sum	297800

A statistics teachers wants to see if a student's final exam score is related to his/her midterm exam score and wants to use that in the future to predict final exam score after the midterm exam is graded. Using the results of the linear regression analysis below, what is the coefficient of determination (R2)? Source df SS p-value Regression 1 2933.9579 2933.9579 13.1322 0.0011 Residual 30 6702.5109 223.4170 Total 31 9636.4688 MS F

$R^{2}=\frac{SS_{Regression}}{SS_{Total}}=\frac{2933.9579}{9636.4688}=0.3044=0.30$

A statistics teachers wants to see if a student's final exam score is related to his/her midterm exam score and wants to use that in the future to predict final exam score after the midterm exam is graded. Using the results of the linear regression analysis below, what is the standard error (Se)? df 13.1322 p-value 0.0011 Source Regression Residual Total 1 30 31 SS MS 2933.9579 2933.9579 6702.5109 223.4170 9636.4688 Select one: 6.642 Se=square root ( Ms_residuals) = square root (223.4170)=14.947 None of these are correct 3.707 14.94 8.542

Suppose you have data from 2018 MLB season and run a linear regression model to predict the Number of Wins (Y) for a team based upon their number of Runs, Hits, Walks, Errors, and Saves. Using the following output, what is the adjusted R-squared? 2018 Team Arizona Atlanta Baltimore Runs 720 1 753 782 Hits 1403 1439 1538 Walks Errors Saves Wins 451 113 3 3 82 586 107 28 72 687 100 2968 79 Texas Toronto Washington 752 1525 625 7141330467 641 1496 588 99 33 8440 96 27 59 Regression Statistics Multiple R 0.9571 R Square 0.9160 Adjusted R Square Standard Error 3.5456 Observations 30 df p-value 0.00000 Source Regression Residual Total SS MSF 5 3288.28204 657.65641 52.31294 24 301.71796 12.57158 29 3590

$R_{Adj}^{2}=1-\frac{(1-R^{2})(n-1)}{n-p-1}$

$R_{Adj}^{2}=1-\frac{(1-R^{2})(n-1)}{n-p-1}$

p=number of predictos = 5( in table)  , n=30, R-square = 0.9160

$R_{Adj}^{2}=1-\frac{(1-0.9160)(30-1)}{30-5-1}$

$R_{Adj}^{2}=0.8985$

Suppose you take a random sample of 36 local houses and build a linear regression moder to predict the appraised value using the living area (in square feet), number of bedrooms, and number of bathrooms. Using the partial printouts below, which of the following is true? Coefficients Intercept 153000 95.856 Beds 3556.89 Baths 1920.2 Sqft

options are not mentioned

Suppose you take a random sample of 20 used sedans and want to build a linear regression model to predict the selling price. You have data on both the age and mileage of the sedans as potential predictors. Using the partial printouts below, which model appears to be best for prediction: Model 1: AGE Model 2: MILES Model 3: AGE and MILES Adjusted R-sq 0.8483 Adjusted R-sq 0.5525 Adjusted R-sq 0.8204 Std Error 1475.4328 Std Error 2382.1169 Std Error 1509.0285 Observations 20 Observations Observations 20 20

The here we have three models,

The criteria for the best model selection is R-Square, the larger value of the R-square the model is best.

among the three models "Model 1: AGE" has the highest R-square value as compared to the other two models.

ANS: "Model 1: AGE" because of high R-square=0.84

Thanks