# Parameter estimates: intercept

Parameter estimates:

intercept: 14179.871 3298.484 4.30 0.0003* (estimate Std ErrortRatio Prob>t )

InCostAid: 0.7768753 0.254022 3.06 0,0058* (estimateStd Error tRatio Prob>t )

Baruch College has substantially less average debt compared tothe other schools with similar in-state costs. Figure 10.13contains JMP output for the simple linear regression of AveDebt onInCostAid with this case removed.

a) State the least-squares regression line.

b) The University of North Florida is one school in this sample.It has an in-state cost of $11,421 and average debt of $17,617.What is the residual?

c) Construct a 95% confidence interval for the slope. What doesthis interval tell you about the change in average debt for a $1000change in the in-state cost?

ans:

a) y = 0.7768753InCostAid+14179.871

b) 0.7768*11421+14179.871 = 23052.5628

residual = 23052.5628 – 17617 =5435.562801

c) 0.7768753+- t*0.254022 = 0.7768753+- 2.073873*0.254022 =

(0.2500659328, 1.303684667)

Baruch College was removed from this analysis because it wasdeemed an outlier. Let’s investigate its impact on the fit.

A) Refit the model using the entire sample of 25 schools. Createa table that summarizes the model estimates with and without thiscase.

B) Describe the impact this observation has on the fit of thelinear regression model.

C) If you were writing a report for publication, would youinclude the fit with or without this case? Explain your answer.

**Need answer for A, B, C**

Answer:

Ans. Suppose in my 25 observation sample data I want to keepvariable like incercept , IncostAid(x) , average debt (y) for myregression model. I want to do a regression analysis between x(incostaid) & y (average debt) on SPSS. Please look at my datafirst. Suppose Intercept is 14,180 for my case.

Now I want to update the image of caculations of the predictedvalue of average debt (ybar) & residuals in each data. pleaselook at the data

A). ans.

From the above image you can easily get know that Error =Observed (y) – Predicted (y)

B) ans. Now impact of the observations on the model , to see itwe need to understand the entire regression result. Please look atthe image below :-

From the above result we easilysee that from the first table that Rsquare = 0.44.

So, 44% of the fitted model is good.

From the anova table we can see that Total variation of theaverage debt is 6657172.5 and among that 2932067.36 are defined byIncostaid & rest are errors.

Our null hypothesis in this regression is H0 : Beta = 0

alternative Ha : Beta 0

By seeing the p-value from co-efficients table of regressionresult (sig. column) , which is 0.000 , we could decide to rejectnull that is Beta = 0. Also we can see it from the value of anaovatable.

Lastly from the residual statistics table we get the entiredescriptive statistics for the residuals.

C)ans. The model Rsquare = 0.44. So, only 44% is of Average Debtis defined by Incostaid. Now I would like to find some otherpredictor variables , which are caused for Average _Debt. Then runa regression. It would help me to get a high R values for moresignificant variable.