Step 1: The least-squares line for predicting mean Mathematics SAT score from me

Question

Step 1:
The least-squares line for predicting mean Mathematics SAT score from mean teacher salary for only the cases where the percent taking is above 40% is MathSAT = __Answer 1__ + __Answer 2__ (TeachSal). Round Answer one to 2 decimal places and Answer two to 5 decimal places.

Answer 1
Answer 2

Step 2:
For states where the percent taking is above 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by _____ points, on average. Round your answer to 5 decimal places.

Step 3:
For states where the percent taking is below 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by _____ points, on average. Round your answer to 3 decimal places

________________________________________________ Data Set listed below

The data set “tchsal2” gives the mean Mathematics SAT score and mean salary of teachers in each of the 50 states and the District of Columbia in 2013. It also includes a categorical variable, pct. taking, that indicates whether the percentage taking is above 40% (Y) or below 40% (N).

Step 1:
The least-squares line for predicting mean Mathematics SAT score from mean teacher salary for only the cases where the percent taking is above 40% is MathSAT = __Answer 1__ + __Answer 2__ (TeachSal). Round Answer one to 2 decimal places and Answer two to 5 decimal places.

Answer 1
Answer 2

Step 2:
For states where the percent taking is above 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by _____ points, on average. Round your answer to 5 decimal places.

Step 3:
For states where the percent taking is below 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by _____ points, on average. Round your answer to 3 decimal places

________________________________________________ Data Set listed below

   MathSAT Avg. teacher salaries 2013 Pct. taking Alabama 534 47,949 N Alaska 505 65,468 Y Arizona 528 49,885 N Arkansas 570 46,632 N California 512 69,324 Y Colorado 581 49,844 N Connecticut 512 69,766 Y Delaware 457 59,679 Y DistColumbia 466 70,906 Y Florida 490 46,944 Y Georgia 487 52,880 Y Hawaii 504 54,300 Y Idaho 459 49,734 Y Illinois 617 59,113 N Indiana 500 51,456 Y Iowa 601 51,528 N Kansas 595 47,464 N Kentucky 584 50,326 N Louisiana 553 51,381 N Maine 467 48,119 Y Maryland 500 65,265 Y Massachusetts 529 73,129 Y Michigan 610 61,560 N Minnesota 608 56,268 N Mississippi 547 41,994 N Missouri 595 47,517 N Montana 540 49,999 N Nebraska 583 48,931 N Nevada 494 55,957 Y NewHampshire 528 55,599 Y NewJersey 522 68,797 Y NewMexico 545 46,573 N NewYork 501 75,279 Y NorthCarolina 506 45,947 Y NorthDakota 609 47,344 N Ohio 556 58,092 N Oklahoma 569 44,128 N Oregon 520 58,758 Y Pennsylvania 504 63,521 Y RhodeIsland 490 63,474 Y SouthCarolina 487 47,924 Y SouthDakota 601 39,580 N Tennessee 569 48,289 N Texas 499 48,110 Y Utah 566 49,393 N Vermont 519 52,526 Y Virginia 514 49,869 Y Washington 523 53,571 Y WestVirginia 501 46,405 N Wisconsin 604 55,171 N Wyoming 588 57,920 N

Explanation / Answer

Regression was calculated separately for Y and N groups.

Step 1:

The least-squares line for predicting mean Mathematics SAT score from mean teacher salary for only the cases where the percent taking is above 40% is MathSAT = __Answer 1__ + __Answer 2__ (TeachSal). Round Answer one to 2 decimal places and Answer two to 5 decimal places.

Answer 1: 471.82

Answer 2: 0.00048

Step 2:

For states where the percent taking is above 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by 0.00048 points, on average. Round your answer to 5 decimal places.

Regression Analysis

r²

0.047

n

26

r

0.216

k

1

Std. Error

20.254

Dep. Var.

MathSAT

ANOVA table

Source

SS

df

MS

F

p-value

Regression

481.05050420

1  

481.05050420

1.17

.2896

Residual

9,844.98795734

24  

410.20783156

Total

10,326.03846154

25  

Regression output

confidence interval

variables

coefficients

std. error

t (df=24)

p-value

95% lower

95% upper

Intercept

471.82

26.1517

18.042

1.83E-15

417.8419

525.7907

Avg. teacher salaries 2013

0.00048

0.00044322

1.083

.2896

-0.00043479

0.00139473

Step 3:

For states where the percent taking is below 40%, increasing the average teacher salary by $1 increases the mean Math SAT score by 0.002 points, on average. Round your answer to 3 decimal places

Regression Analysis

r²

0.128

n

25

r

0.358

k

1

Std. Error

28.781

Dep. Var.

MathSAT

ANOVA table

Source

SS

df

MS

F

p-value

Regression

2,805.6083

1  

2,805.6083

3.39

.0787

Residual

19,051.7517

23  

828.3370

Total

21,857.3600

24  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=23)

p-value

95% lower

95% upper

Intercept

472.80

55.3741

8.538

1.38E-08

358.2521

587.3522

Avg. teacher salaries 2013

0.00202

0.0011

1.840

.0787

-0.0003

0.0043

Regression Analysis

r²

0.047

n

26

r

0.216

k

1

Std. Error

20.254

Dep. Var.

MathSAT

ANOVA table

Source

SS

df

MS

F

p-value

Regression

481.05050420

1  

481.05050420

1.17

.2896

Residual

9,844.98795734

24  

410.20783156

Total

10,326.03846154

25  

Regression output

confidence interval

variables

coefficients

std. error

t (df=24)

p-value

95% lower

95% upper

Intercept

471.82

26.1517

18.042

1.83E-15

417.8419

525.7907

Avg. teacher salaries 2013

0.00048

0.00044322

1.083

.2896

-0.00043479

0.00139473

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