What is the percentage of the variance of the Avg. Total Score variable explained by this...

What is the percentage of the variance of the Avg. Total Score variable explained by this linear relationship with per pupil spending? Briefly explain your answer.
Interpret the slope of the regression line for this model.

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

Expert Solution

We will be applying the Linear regression model here, it can be done by using the function LINEST(y_value, x_value, TRUE, TRUE) where y_values contain values of Sales here and x_values have Advertising values.

Select 5 rows and 2 columns and then write the formula in the first cell and after that, press Shift + Ctrl + Enter.

The equation comes out to be -

avg tot score = 1053.703 + 5.616*PPS -3.37*T/S Ratio + 1.382*Avg Salary - 2.90 * %Taker s

The slopes for the regression line will be 5.616, -3.37, 1.38 and -2.90 for PPS, T/S Ration, Avg Salary and %Taker s respectively.

Interpretation of slopes

When PPS is increased by a unit, the avg total will increase by 5.616 units.

When T/S Ratio is increased by a unit, the avg total will decrease by 3.37 units.

When Avg Salary is increased by a unit, the avg total will increase by 1.382 units.

When %Taker s is increased by a unit, the avg total will decrease by 2.9 units.

The coefficient of determination(R**2) comes out to be 0.824190568, it means 82.4% of the avg total score variable can be explained by all the independent variables.

orchestra answered 2 years ago

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