%Takers Avg. Tot. Score [1,] \"Alabama\" 10 1033 [2,] \"Alaska\" 48 938 [3,] \"A

Question

%Takers   Avg. Tot. Score
[1,] "Alabama"    10   1033
[2,] "Alaska"     48   938
[3,] "Arizona"    28   948
[4,] "Arkansas"     7   1009
[5,] "California"     46   906
[6,] "Colorado"     31   984
[7,] "Connecticut"    82   912
[8,] "Delaware"     70   901
[9,] "Florida"    50   893
[10,] "Georgia"    66   858
[11,] "Hawaii"     58   893
[12,] "Idaho"    16   983
[13,] "Illinois"     14   1052
[14,] "Indiana"    59   886
[15,] "Iowa"     7   1103
[16,] "Kansas"     11   1064
[17,] "Kentucky"     12   1003
[18,] "Louisiana"    10   1025
[19,] "Maine"    70   900
[20,] "Maryland"     65   913
[21,] "Massachusetts"    81   911
[22,] "Michigan"     13   1037
[23,] "Minnesota"    10   1089
[24,] "Mississippi"    5   1040
[25,] "Missouri"     10   1049
[26,] "Montana"    23   1013
[27,] "Nebraska"     10   1054
[28,] "Nevada"     31   921
[29,] "New Hampshire"    70   939
[30,] "New Jersey"     72   902
[31,] "New Mexico"     12   1019
[32,] "New York"     76   896
[33,] "North Carolina"   62   869
[34,] "North Dakota"     7   1111
[35,] "Ohio"     25   979
[36,] "Oklahoma"     11   1031
[37,] "Oregon"     53   951
[38,] "Pennsylvania"     72   884
[39,] "Rhode Island"     70   892
[40,] "South Carolina"   60   848
[41,] "South Dakota"     6   1072
[42,] "Tennessee"    14   1044
[43,] "Texas"    50   897
[44,] "Utah"     6   1080
[45,] "Vermont"    70   905
[46,] "Virginia"     66   900
[47,] "Washington"     50   941
[48,] "West Virginia"    19   936
[49,] "Wisconsin"    10   1077
[50,] "Wyoming"    12   1005

We wish to construct a regression model to predict Avg. Total Score from %Takers.

1. Consider the t test of the slope. How many degrees of freedom are used for this t test?

2 .Show that the T-value is equal to the slope divided by the standard error of the slope. Briefly explain why this is so.

3. Assuming it to be valid, interpret the result of the t test of the slope. Under what conditions is it valid?

4. Using the t test output, compute by hand a 95% Confidence Interval for the population slope.

Explanation / Answer

we will answer this question with the help of minitab spftware

the table of regression is

The regression equation is
Y = 1061 - 2.49 x

Predictor Coef SE Coef T P
Constant 1061.19 8.40 126.26 0.000
x -2.4855 0.1857 -13.39 0.000

S = 34.7484 R-Sq = 78.9% R-Sq(adj) = 78.4%

Analysis of Variance

Source DF SS MS F P
Regression 1 216350 216350 179.18 0.000
Residual Error 48 57958 1207
Total 49 274308

hence df=1

b) t-value=-13.39=1-=-2.4855/.1857=estimate/SE

this is because df=1

3) p-vale for slope is 0 <0.05 hence we can colclude that the slope has significant effect on regression

4) the 95% CI for slope is

( -2.858798 -2.11213)

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