Question

4. The average gasoline price per gallon (in cities) and the cost of a barrel o! shown below for a random selection of weeks from 2009-2010. The following quanti- Table 1: Oil and Gasoline X: Oil (8) 84.32 58.93 56.44 73.38 50.66 47.73 Y: Gasoline($) 2.976 2.516 2.677 2.728 2.360 2.420 ties have been computed for your convenience: u = 371.46, y = 15.68, 12 = 23997.29, y = 41.22 and ry 985.54. =0.9291 0.05 - 2.776 Compute the sample correlation coefficient r = For testing H:p=0 vs H:#0, compute the test stati tatistic:t: 5.024 Determine the critical values at a = Is the population correlation coefficient significantly different from zero? Yes Compute the estimated regression line (least squares estimate), the intercept a = 1.69 and the slope b =0.015 Predict the gasoline price when the oil cost is $70:52.74
i need someone to dumb this down, and explain in detail how to solve tnis.. thank you

Answer 1

sal where - 985.54 en (Emy) - (2x) (y) ✓[n (8x²) - (Ex)²] [n (E9²)-(Ey) 2] Eny Ex= 37.46, Ey-15.68 {x² = 23997.29 Ey² = 41.22 r = 6(985.54) - (371-46 (15.68) number -paints [6(23997.28) -371.46)][6141.22) - 15.6872 & n=6 af data 91二 0.929L means mean Ho: f= 0 vs H,: 870 test statistic t = run-z (t leas degree of theledom XI-92 af = n-2=6-2=4 t = 0.g2giru VI -(0.929))2 t = 5.0244 x 5.024 critical value of & at dF =4 is given by totable le, te = 2.78 t> tc, which we have to reject null hypothesis correlation coefficient (papulation) is significantly different from zero. slope ny (24) 6 1985.54)-(371-46)(1518) nen? (Ex)2 6(23997.29)-(37.46) slope 0.0149 Z 0.015 = b tercept EY - {x)b (15.68) - (371.460.015 6 1-6858 1.69 regression line a + bx = 1.69+ 0.015X when all cast is 70$ , x=70 the gasoline price =ý will be, ŷ = 1.69 +0.015 (70) = 2.734 5 - 2.139 estmate