a) Regression model of researcher A has a better explanatory power because of following conditions compared to researcher B
-The independent variable P in the first model is significant at 1% and 5%.but in the case of second case none of the independent variables are significant at 1%,5% and 10%(P values are insignificant)
-In the second case, There exists multicollinearity ie there is strong colinearity among the predictors. It is given that the sample correlation coefficient among predictors H and P is .98 which shows a high positive correlation.
-When multicollinearity exists among predictors in a model there is chances for the t ratios of the coefficients to be statistically insignificant and R square which will measure the overall measure of goodness of fit to be very high.
Here the t ratios are insignificant for all coefficients including constant as a result of the presence of multicollinearity. In both models, the r square is the same but in the second model, the r square can be high due to multicollinearity. So regression model by researcher a has better r square which is free from multicollinearity.
b) The assertion cannot be said correctly because the model has certain limitations. The first model shows that the R variable has insignificant t ratio. This coefficient has insignificant t ratios because they do not have an impact on the dependent variable or cannot be proved statistically. here both models have very low r square which indicates the overall measure of goodness of fit is very low.
There is a negative weak correlation between the hours of revision and hours on the primary study
c)The assertion of the researcher b is wrong because he has chosen the wrong combination of predictors. He could have chosen the predictors H and R which would have avoided the multicollinearity problem that exists in the present model.
d)It is true what the commentator has said. There exist multicollinearity problem between the H and P and this led to the negative coefficient of P.Existence of multicollinearity have led to the insignificance of the t ratios in the second model
6. Two researchers are investigating the effects of time spent studying on the examination marks earned by studen...
6. Two researchers are investigating the effects of time spent studying on the examination marks earned by students on a certain course. For a sample of 100 students, they have the examination mark, M, total ours spent studying, H, on revision. R. By definition, H = P+ R. The sample means of H. P. and R are 100 hours, 95 hours, and 5 hours, respectively. The sample correlation coefficients are 0.98 for H and P, and 0.10 for H and...
Table 6 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown. Note: 2.051E - 05 = 2.051 ∗ 10-05 and...
What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time Score 3 10 15 512 015 58 75 89 89 77 79 54 96 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? - 0 H: 70 (Round to four The p-value is: decimal places) c. Use a...
What is the relationship between the amount of time statistics students study per week and their final exam scores? The results of the survey are shown below. Time Score 3 67 13 95 6 15 77 89 13 100 3 66 7 63 11 79 1 59 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? D = 0 H: ? *0 The p-value is: (Round...
please correct red error boxes
What is the relationship between the amount of time statistics students study per week and their final exam scores! The results of the survey are shown below The ruil and alternative hypotheses for correlation are The preluet: 1.0024 Round to four decimal places c. Use a level of sigrice -0.05 to state the conclusion of the hypothesis test in the context of There la statistically significant evidence la conclude that there a carrodation between the...
Need help for #4 and #6 please show work and explain
90% 10:41 AM PROBLEMS 263 In this dstribation, r sample mean of M-70 comesponds to a bscvee od STEP 4 Make a dechion about He and stale the conclmion The -score we oblained is in the critical region. This indicaes that our sample mean of M-0 is not an estreme orumsual value beeteaned from a population with μ-65. Therefore. our santa decision is to Fail a rejiecr He Our...