Question: By hand and using software, how would I set up and solve the normal equation (A T Ax = A T b) for the linear

By hand and using software, how would I set up and solve the normal equation (A^T Ax = A^T b) for the linear regression (least square) given a data set of years (from year zero) and populations (starting from 159) in a geographic area, with numbers like the following:

0159

1161

2163

3166

4169

5172

6175

7178

8181

9184

10187

11190

12192

13195

14197

15200

16202

17204

18206

19208

20210

21211

22213

23215

24217

25219

26221

27223

28225

29228

30230

31232

32234

33236

34239

35241

36243

37245

38248

39250

40253

41255

42257

43260

44263

45266

46269

47272

48276

49279

50282

51285

52288

53290

54293

55295

56298

57301

58303

59306

60309

61311

62313

63316

64318

65320

66322

67324

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