A researcher collected a sample of 12 observations in a multiple regression study focusing on two independent variables (X1 and X2). The following partial results were observed: SST = 15200 SSE = 4800 SSR(X1) = 5700 SSR(X2) = 6700At the 1% level of significance, what decision should be made when testing the null hypothesis that variable X1 does not significantly improve the model after variable X2 has been accounted for?（R for reject the null hypothesis, N for not reject it)

A sample of 12 observations collected in a multiple regression study on two independent variables (X1 and X2) shows the following partial results. SST = 12321 and SSE = 3516. If SSR(X1) = 4496 and SSR(X2) = 5378, and you would like to test the null hypothesis that variable X1 does not significantly improve the model after variable X2 has been included, what would be the critical value of F at the 5% level of significance?

A sample of 12 observations collected in a multiple regression study on two independent variables (X1 and X2) shows the following partial results. SST = 12321 and SSE = 3516. If SSR(X1) = 4496 and SSR(X2) = 5378, what would be the value of the partial F test statistic used to test the null hypothesis that variable X1 does not significantly improve the model after variable X2 has been included? Round your final answer to two decimal places.

For a sample of 30 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in $1,000). A portion of the regression results shows that the coefficients for poverty and average income are 54.22 and 5.10, respectively. Based on this information, what statistical decision should be made when testing the null hypothesis that X1 has no significant effect on Y at the 1% level of significance? Assume the standard error of the slope of Y with variable X1 equals 20.50. Note: Y = crime rate in each city (crime per 100,000 residents); X1 = poverty rate (in %); and X2 = average income (in $1,000). a. Do not reject the null hypothesis. b. Accept the alternative hypothesis. c. Accept the null hypothesis. d. Reject the null hypothesis.

Suppose we are conducting a hypothesis test with the following hypotheses:H0: p = 0.7H1: p > 0.7Furthermore suppose we get a p-value of 0.07 while using = 0.05, which of the following is the correct decision?a.At the 5% level of significance, there is significant evidence to reject H1 and retain H0.  b.At the 5% level of significance, there is significant evidence to retain H0c.At the 5% level of significance, there is significant evidence to reject H0 in favour of H1.  d.At the 5% level of significance, there is not significant evidence to reject H0.

A significance test of H: B = 0 against the two-sided alternative H: B # 0, where B = the slope of the population least-squares regression line for predicting Ethereum price from Bitcoin price, was conducted at the 5% significance level. Which of the following gives the correct decision for the significance test and the possible error that could result from this decision? (A) Fail to reject the null hypothesis; Type I error (B) Fail to reject the null hypothesis; Type II error (C) Reject the null hypothesis; Type I error (D) Reject the null hypothesis; Type II error (E) Reject the null hypothesis; either Type I error or Type Il error is possible