PLEASE help with FINISH PROBLEM. WILL THUMBS UP IF CORRECT. The following data is representative of that reported in an article with \( x = \) burner-area liberation rate (MBtu/hr-ft\(^2\)) and \( y = \) NO\(_x\) emission rate (ppm):\[\begin{array}{c|cccccccccccc}x & 100 & 125 & 125 & 150 & 200 & 250 & 250 & 300 & 300 & 350 & 400 & 400 \\y & 140 & 130 & 170 & 210 & 200 & 290 & 320 & 490 & 300 & 610 & 620 & 670 \\\end{array}\]**(a)** Does the simple linear regression model specify a useful relationship between the two rates? Use the appropriate test procedure to obtain information about the P-value, and then reach a conclusion at significance level 0.01. State the appropriate null and alternative hypotheses.- \( H_0: \beta_1 = 0 \)- \( H_a: \beta_1 \neq 0 \) (Selected Option)Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)- \( t = \) [Blank]- P-value = [Blank]State the conclusion in the problem context.- \(\bullet\) Reject \( H_0 \). There is evidence that the model is useful. (Selected Option)**(b)** Compute a 95% CI for the expected change in emission rate associated with a 10 MBtu/hr-ft\(^2\) increase in liberation rate. (Round your answers to two decimal places.)- ( [Blank], [Blank] ) ppm

Dependent variable (y) NOx emission rate Independent variable (x) burner area libeartion rate The steps in excel for simple linear regression analysis are1) Open Excel 2) Enter Data2)Go to Data > Data analysis > select regression 3) Select y input range and x input range4)click on labels 5) select output range 6) click ok The excel data analysis tab output is a) Test for significance of slopeThe null and alternative hypothesis is Option B is correctThe value of the test statistic t is 18.04 from excel output The p-value of the test is 0.000Decision: Reject Ho since p-value < Conclusion: There is sufficient evidence to conclude that the model is usefullOption A is correct b) The value of the slope is 1.7482 The expected change in emission rate associated with 10 MBtu \ hr increase in liberation rate is The 95% confidence interval for the expected change in emission rate associated with 10 MBtu \ hr increase in liberation rate is The 95% confidence interval for the expected change in emission rate associated with 10 MBtu \ hr increase in liberation rate is (17.27, 17.69) The 95% confidence interval for the expected change in emission rate associated with 1MBtu \ hr increase in liberation rate is (1.54, 1.96) From Excel output a) The value of the test statistic t is 18.04 The p-value of the test is 0.000Conclusion: There is sufficient evidence to conclude that the model is usefullb) The 95% confidence interval for the expected change in emission rate associated with 10 MBtu \ hr increase in liberation rate is (17.27, 17.69)