Question

i need help with question 15.1 (all the questions) a-g

15.1 The results of a multiple regression based on nine observations are shown in Table 15.11. Based on these results answer the following questions: a. What percentage of variance is explained by the regression? TABLE 15.11 Results of a Multiple Regression Analysis Shi 1.3 2.7 0.5 5.0 3.6 1.8 0.6 8.3 Intercept 75.3 Coefficient of multiple correlation 0.95 Standard deviation of errors 12.0 F-value 14.1 b. Is the regression significant at the 90% confidence level? c. Which variable has the highest coefficient? d. Which variable is most significant? e, which parameters are not significant at 90%? f. What is the problem with this regression? g. What would you try next?

Answer 1

$a.~Percentage~of~variation~is~explained~by~the~regression\\ =(0.95)^2*100=90.25\%\\ b.~Critical~value=F_{0.1,4,4}=4.1073\\ The~regression~is~significant~since~F-value> 4.1073.\\ c.~variable~4~i.e.~j=4~has~the~the~highest~coefficient.\\ d.~p-value~Variable~1=2P(t>1.3/3.6|t\sim t_4)= 0.7363\\ p-value~Variable~2=2P(t>2.7/1.8|t\sim t_4)= 0.208\\ p-value~Variable~3=2P(t>0.5/0.6|t\sim t_4)=0.4515\\ p-value~Variable~4=2P(t>5.0/8.3|t\sim t_4)=0.5794\\ Variable~2~is~most~significant.\\ e.~Since~p-value~for~all~Variables>0.1~hence~all~are~insignificant~at~10\%~level.\\ f.~Adjusted~R^2=1-(0.9025)*((9-1)/(9-(4+1)))=-0.805\\ Negative~ Adjusted ~R^2~ appears~ when~ Residual ~sum~ of ~squares~ approaches\\ to~ the~ total ~sum~ of~ squares,~ that ~means~ the~ explanation ~towards~ response\\ ~ is~ very~ low~ or~ negligible~. Hence~ explanatory ~variables~are~insignificant.\\ g.~To~explore ~the~other~functional~relationship~between~dependent~and\\~independent~variables.$