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