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
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)
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