NOTE: I don\'t understand how to get the least square equations for 40%. This wa
ID: 3050366 • Letter: N
Question
NOTE: I don't understand how to get the least square equations for 40%. This was answered already on the boards. I have Minitab express.
SAT scores and teacher salaries, continued. 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).
(a)Find 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%. Interpret the slope in the context of the problem.
(b)Find the least-squares line for predicting mean Mathematics SAT score from mean teacher salary for only the cases where
(c) If you did Problem 3 (above), compare your results with those in part (a) of Problem 4. What do you conclude? (Hint: Think of slope and Simpson’s Paradox)
i MathSAT Avg. teacher salaries 2013 Pct. taking
Alabama 534 47949 N
Alaska 505 65468 Y
Arizona 528 49885 N
Arkansas 570 46632 N
California 512 69324 Y
Colorado 581 49844 N
Connecticut 512 69766 Y
Delaware 457 59679 Y
DistColumbia 466 70906 Y
Florida 490 46944 Y
Georgia 487 52880 Y
Hawaii 504 54300 Y
Idaho 459 49734 Y
Illinois 617 59113 N
Indiana 500 51456 Y
Iowa 601 51528 N
Kansas 595 47464 N
Kentucky 584 50326 N
Louisiana 553 51381 N
Maine 467 48119 Y
Maryland 500 65265 Y
Massachusetts 529 73129 Y
Michigan 610 61560 N
Minnesota 608 56268 N
Mississippi 547 41994 N
Missouri 595 47517 N
Montana 540 49999 N
Nebraska 583 48931 N
Nevada 494 55957 Y
NewHampshire 528 55599 Y
NewJersey 522 68797 Y
NewMexico 545 46573 N
NewYork 501 75279 Y
NorthCarolina 506 45947 Y
NorthDakota 609 47344 N
Ohio 556 58092 N
Oklahoma 569 44128 N
Oregon 520 58758 Y
Pennsylvania 504 63521 Y
RhodeIsland 490 63474 Y
SouthCarolina 487 47924 Y
SouthDakota 601 39580 N
Tennessee 569 48289 N
Texas 499 48110 Y
Utah 566 49393 N
Vermont 519 52526 Y
Virginia 514 49869 Y
Washington 523 53571 Y
WestVirginia 501 46405 N
Wisconsin 604 55171 N
Wyoming 588 57920 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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