Question

In: Statistics and Probability

Using Minitab to calculate the regression analysis: avg tot. score vs pps. Then, Compute and interpret...

Using Minitab to calculate the regression analysis: avg tot. score vs pps. Then,

Compute and interpret a 95% confidence interval for the population slope.

State PPS T/S Ratio Avg. Salary %Takers Avg. Tot. Score
"Alabama"        4.405 17.2 31.144 10 1035
"Alaska"         8.963 17.6 47.951 48 939
"Arizona"        4.778 19.3 32.175 28 950
"Arkansas"       4.459 17.1 28.934 7 1010
"California"     4.992 24 41.078 46 908
"Colorado"       5.443 18.4 34.571 31 985
"Connecticut"    8.817 14.4 50.045 82 914
"Delaware"       7.03 16.6 39.076 70 902
"Florida"        5.718 19.1 32.588 50 895
"Georgia"        5.193 16.3 32.291 66 859
"Hawaii"         6.078 17.9 38.518 58 895
"Idaho"          4.21 19.1 29.783 16 984
"Illinois"       6.136 17.3 39.431 14 1054
"Indiana"        5.826 17.5 36.785 59 887
"Iowa"           5.483 15.8 31.511 7 1105
"Kansas"         5.817 15.1 34.652 11 1066
"Kentucky"       5.217 17 32.257 12 1005
"Louisiana"      4.761 16.8 26.461 10 1027
"Maine"          6.428 13.8 31.972 70 902
"Maryland"       7.245 17 40.661 65 915
"Massachusetts" 7.287 14.8 40.795 81 913
"Michigan"       6.994 20.1 41.895 13 1038
"Minnesota"      6 17.5 35.948 10 1091
"Mississippi"    4.08 17.5 26.818 5 1041
"Missouri"       5.383 15.5 31.189 10 1051
"Montana"        5.692 16.3 28.785 23 1014
"Nebraska"       5.935 14.5 30.922 10 1056
"Nevada"         5.16 18.7 34.836 31 922
"New Hampshire" 5.859 15.6 34.72 70 941
"New Jersey"     9.774 13.8 46.087 72 904
"New Mexico"     4.586 17.2 28.493 12 1021
"New York"       9.623 15.2 47.612 76 898
"North Carolina" 5.077 16.2 30.793 62 871
"North Dakota"   4.775 15.3 26.327 7 1113
"Ohio"           6.162 16.6 36.802 25 981
"Oklahoma"       4.845 15.5 28.172 11 1032
"Oregon"         6.436 19.9 38.555 53 953
"Pennsylvania"   7.109 17.1 44.51 72 885
"Rhode Island"   7.469 14.7 40.729 70 894
"South Carolina" 4.797 16.4 30.279 60 849
South Dakota"   4.775 14.4 25.994 6 1074
"Tennessee"      4.388 18.6 32.477 14 1045
"Texas"          5.222 15.7 31.223 50 899
"Utah"           3.656 24.3 29.082 6 1082
"Vermont"        6.75 13.8 35.406 70 907
"Virginia"       5.327 14.6 33.987 66 902
"Washington"     5.906 20.2 36.151 50 943
"West Virginia" 6.107 14.8 31.944 19 937
"Wisconsin"      6.93 15.9 37.746 10 1079
"Wyoming"        6.16 14.9 31.285 12 1006

Solutions

Expert Solution

The 95% confidence interval for the population slope is between -35.5995 and -6.0984.

We are 95% confident that the true regression slope is between -35.5995 and -6.0984.

The output is:

0.144
r   -0.380
Std. Error   69.985
n   50
k   1
Dep. Var. Avg. Tot. Score
ANOVA table
Source SS   df   MS F p-value
Regression 39,557.8739 1   39,557.8739 8.08 .0066
Residual 2,35,102.3061 48   4,897.9647
Total 2,74,660.1800 49  
Regression output confidence interval
variables coefficients std. error    t (df=48) p-value 95% lower 95% upper
Intercept 1,094.6985
PPS -20.8490 7.3363 -2.842 .0066 -35.5995 -6.0984

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