This is a regression chart. Please show me the formulas for lower 95% and upper

Question

This is a regression chart. Please show me the formulas for lower 95% and upper 95%. And also please tell me how to find the p-value. (the areas are marked red with a red question mark)

Please show all work.

Quiz03dFinish.xlsx 1 SUMMARY OUTPUT X Variable 1 Residual Plot 3 Regression Statistics 4 Multiple F 0.707107 5 R Square 6 AdjustedI 0.333333 7 Standard 0.57735 8 Observati 0.5 0.5 .5 0.5 0.5 0.5 X Variable 1 10 ANOVA nificance F 3 0.18169 MS 12 Regressio 13 Residual 14 Total 15 16 17 Intercept 18 X Variable 19 1 0.333333 4 Coefficientandard Err t Stat P-value Lower 95%U per 95%ower 95.09 er 95.0% 1 0.258199 -3.87298 0.030466 -1.8217-0.1783 -1.8217-0.1783 0.5 0.288675 1.732051 0.18169 -0.41869 1.418693 -0.41869 1.418693 21 22 RESIDUAL OUTPUT 23 24 ObservatioPredicted Y Residuals 25 26 27 -0.5 0.5 0.5 0.5 1.5 1.5 0.5 -0.5 29

Explanation / Answer

So,

p-value comes from the Z value.

Z is got from the hypoothesis testing of coefficient of X variable

Z= X-Mu /SE = (.5-0)/.288675 = 1.732, we are testing for statisitcally significane of this variable

Since this is just 1 variable , statistical significant is calculated as statistical significance of model

So, at df num = 1, df denominator = 3, and F value of .18169, we have a p-value of .18169

So, the Lower and Upper 95% CI is given by :

Upper cutoff= Betacoeff of X1 + TINV( alpha, n) * SE

= 0.5 + TINV(0.05, 3) * .288675

= 1.41869

Higher cutoff= Betacoeff of X1 - TINV( alpha, n) * SE

= 0.5 - TINV(0.05, 3) * .288675

= -.41869

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