How is grit related to an individual's overall personal achievement, which includes income, happiness, health, family and friendship? A government agency has conducted a survey on a simple random sample of individuals on grit and summarised an achievement index for them. A least squares (LS) estimation is applied to estimate the regression model E (Achievement, | Grit;) = Bo + B1 Grit; Some summary statistics are shown in the following table. Grit Achievement mean 65.300 35.461 var 419.426 69.006 COV 157.599 sum of squares 421097 sample size (n) 90 sum of squared residuals 871.166 Use the information to answer all the questions below. (a) Fill the blanks in the regression table. table estimate s.e. t p-value intercept [a] [b] [c] [d] slope [e] [f] [g] [h] In your answer, you may arrange the values as in the above output table or simply write [a]=XXX, ..., [h]=XXX. (b) What is the value of R2 (c) What is the underlying null hypothesis for Bj from the t-statistic in the Table of question (a)? (d) What is the underlying alternative hypothesis for Bj from the p-values in the Table of question (a)? (e) Compute the 99% confidence interval for 1 and explain its interpretation. Show the steps of calculation. (f) Carry out a test to investigate if high Grit is associated with high achievement at 5% significance level. You need to (1) define new notation (if any), (2) briefly justify your testing procedure, (3) state the hypotheses, (4) calculate the test statistic and show your calculation steps, (5) use the p-value approach, (6) make decision for the test and briefly explain