The following problem makes use of the dataset found below:

Part a: Find the equation of the regression line and the coefficient of determination for x & z.

Part b: Determine at the 5% significance level if x can be used to predict z.

Part c: Find the equation of the regression line and the coefficient of determination for y and z. Part d: Determine at the 5% significance level if y can be used to predict z.

x, y, z

19.07380917, -176.6170573, -848.624056

13.60875612, -109.4639292, -524.5676608

34.05744828, -115.764133, -539.3617822

123.4534394, -140.9127576, -566.422735

40.03859089, -96.45214092, -422.3428546

68.27217027, -30.7303964, -78.26186033

129.9417958, -0.783750479, 132.6084684

104.3065357, -179.6552941, -784.5766662

65.23455764, -35.72065147, -110.2526195

74.8357631, -137.5640768, -598.1013244

102.5872457, -175.5739073, -762.0682966

162.2094054, -11.81958957, 108.380905

103.4606848, -37.75915273, -66.78754326

146.5792999, -24.191536, 30.78595755

125.6767996, -128.4307215, -513.9644357

72.40458188, -1.507935065, 73.2254356

98.9398761, -11.30377934, 53.90661328

75.88320902, -172.5365441, -768.0844342

40.74671144, -66.16248068, -288.4297626

175.4893152, -12.16421451, 129.3612848

143.2229182, -0.268768433, 159.1849204

71.36866651, -1.347504643, 74.12870491

74.73228931, -180.1406283, -820.9054561

63.53907514, -104.286689, -454.1715109

162.7599269, -0.000649484, 182.1676508

166.3020767, -30.47992884, 31.17096285

7.696276973, -3.445856065, 5.126255967

58.44292615, -75.4501776, -315.2878175

161.0038872, -161.7236442, -644.0439661

98.82060776, -120.6207256, -500.0104211