1 4 A psychiatrist wants to know whether the level of pathology (Y) in psychotic patients 6 months after treatment can be predicted with reasonable accuracy from knowledge of pretreatment symptom ratings of thinking disturbance (X 1 ) and hostile suspiciousness (X 2 ) The SAS output is given bellow Number of Observations Read 53 Number of Observations Used 53 Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr F Model 2 2753 87136 1376 93568 6 24 0 0038 Error 50 11037 220 74597 Corrected Total 52 13791 Root MSE 14 85752 R Square 0 1997 Dependent Mean 22 69811 Adj R Sq 0 1677 Coeff Var 65 45708 Parameter Estimates Variable DF Parameter Estimate Standard Error tValue Pr t Intercept 1 0 63535 20 96833 0 03 0 9759 x1 1 23 45144 6 83851 3 43 0 0012 x2 1 7 07261 3 01092 2 35 0 0228 1 Write the least square equation given parameter estimate table 2 Calculate the predict value Y if X 1 2 80 and X 2 7 0 3 Is the overall model significant Write the null and alternative hypothesis, F value and conclusion Explain 4 Sums of squares are shown next for three regression models Determine the R 2 values for each of these models If you use R 2 and model simplicity as selection criteria, which model appears to be the best Y regress on X 1 SSY 13 791 2 SSE 12,255 3 Y regress on X 2 SSY 13 791 2 SSE 13,633 3 Y regress on X 1 and X 2 SSY 13 791 2 SSE 11,037 3

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1~4. A psychiatrist wants to know whether the level of pathology (Y) in psychotic patients 6 months after treatment can be predicted with reasonable accuracy

1~4. A psychiatrist wants to know whether the level of pathology (Y) in psychotic patients 6 months after treatment can be predicted with reasonable accuracy from knowledge of pretreatment symptom ratings of thinking disturbance (X₁) and hostile suspiciousness (X₂).The SAS output is given bellow.

Number of Observations Read	53
Number of Observations Used	53

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr>F
Model	2	2753.87136	1376.93568	6.24	0.0038
Error	50	11037	220.74597
Corrected Total	52	13791

Root MSE	14.85752	R-Square	0.1997
Dependent Mean	22.69811	Adj R-Sq	0.1677
Coeff Var	65.45708

Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	tValue	Pr>\|t\|
Intercept	1	-0.63535	20.96833	-0.03	0.9759
x1	1	23.45144	6.83851	3.43	0.0012
x2	1	-7.07261	3.01092	-2.35	0.0228

1.Write the least square equation given parameter estimate table

2.Calculate the predict value Y if X₁=2.80 and X₂=7.0

3. Is the overall model significant? Write the null and alternative hypothesis, F- value and conclusion. Explain.

4. Sums of squares are shown next for three regression models. Determine the R²- values for each of these models. If you use R² and model simplicity as selection criteria, which model appears to be the best?

Y regress on X₁: SSY = 13 791.2 SSE=12,255.3

Y regress on X₂: SSY= 13.791.2 SSE=13,633.3

Y regress on X₁ and X₂: SSY = 13 791.2 SSE=11,037.3