please show me the steps ### Consider the Following Data:| \( x \) | \(-1.1\) | \(4.0\) | \(2.5\) | \(3.0\) | \(-1.3\) | \(1.1\) | \(5.1\) ||----------|----------|---------|---------|---------|----------|---------|---------|| \( y \) | \(2.1\) | \(4.6\) | \(3.2\) | \(1.9\) | \(12.1\) | \(8.1\) | \(3.6\) |#### Find:(a) The least-square linear fit model. (b) The least-square quadratic fit model.

Given- Consider the following data: x -1.1 4.0 2.5 3.0 -1.3 1.1 5.1 y 2.1 4.6 3.2 1.9 12.1 8.1 3.6 To find- Find: The least-square linear fit model. The least-square quadratic fit model.Explanation- By using given data, the table becomes x y x2 xy x3 x4 x2y -1.1 2.1 1.21 -2.31 -1.331 1.4641 2.541 4.0 4.6 16 18.4 64 256 73.6 2.5 3.2 6.25 8 15.625 39.0625 20 3.0 1.9 9 5.7 27 81 17.1 -1.3 12.1 1.69 -15.73 -2.197 2.8561 20.449 1.1 8.1 1.21 8.91 1.331 1.4641 9.801 5.1 3.6 26.01 18.36 132.641 676.5201 93.636 ∑x = 13.3 ∑y = 35.6 ∑x2 = 61.37 ∑xy = 41.33 ∑x3 = 237.079 ∑x4 = 1058.3669 ∑x2y = 237.127Now, a.) We know that, the linear equation is of the form- y = ax + b and The normal form of the equation become ∑y = a∑x + nb∑xy = a∑x2 + b∑x Here n = 7 By putting the values using the table, we get 35.6 = 13.3a + 7b41.33 = 61.37a + 13.3b By solving, we get a = -0.7288 b = 6.4705 Therefore, the linear equation become y = -0.7288x + 6.4705Now, b.) We know that, the quadratic equation is of the form- y = ax2 + bx + c and The normal form of the equation become ∑y = a∑x2 + b∑x + nc∑xy = a∑x3 + b∑x2 + c∑x∑x2y = a∑x4 + b∑x3 + c∑x2 Here n = 7 By putting the values using the table, we get 35.6 = 61.37a + 13.3b + 7c41.33 = 237.079a + 61.37b + 13.3c237.127 = 1058.3669a + 237.079b + 61.37c By solving, we get a = 0.1084 b = -1.0906 c = 6.2074 Therefore, the linear equation become y = 0.1084x2 - 1.0906x + 6.2074Answer: y = -0.7288x + 6.4705 y = 0.1084x2 - 1.0906x + 6.2074