Researchers examined the relationship between two quantitative variables, x and y. We aim to express the relationship between x and y by using the simple linear regression modelYi=0+ 1xi+ Ei.Use the information below to answer the following questions.

x = 696,y = 4498,xy = 177353,x2= 27194,y2= 1195676,n = 18

(a)What is the estimate of the slope coefficient 1?(2 marks)

12.6988

9.4871

14.7005

9.6398

12.1643

(b)What is the estimate of the intercept coefficient 0?(2 marks)

402.3909

111.7256

220.4641

129.0179

278.7612

(c)What is the value of the coefficient of determination?(2 marks)

0.6215

0.5822

0.6922

0.3906

0.9301

(d)Suppose we want to test, at the 5% level of significance, the null hypothesis H0: 1=2 vs the alternative hypothesis Ha:1<2. What is the value of the observed test statistic associated with this test?(2 marks)

5.4979

4.7216

5.1983

4.8932

3.9453

(e)What is the predicted value of ywhen x is equal to37?(2 marks)

90.7933

229.6151

318.2988

10.6982

59.2131

(f)What is the 99% prediction interval for y when x is equal to 42?(2 marks)

(422.6652, 158.2080)

(459.0487, 201.7211)

(128.5554, 390.3297)

(178.5487, 458.0538)

(329.376,251.4971)