The economics research group from Q3 also obtained, from their…
The economics research group from Q3 also obtained, from their random sample of 300 New Zealand adults, data on each individual’s total annual income (rounded to the nearest $1,000) and total debt (rounded to the nearest $1,000). The data are in the file IncomeDebt2022.xls. The research group now wants to investigate the relationship between debt and income.
(a) Construct a scatterplot of Debt vs Income, with Debt on the y-axis.
(b) Describe what the scatterplot in (a) suggests about the relationship between Debt and Income.
(c) Use Excel to find the least squares regression line for predicting debt based on income.
(d) Interpret, in context, the slope coefficient in the model.
(e) Give the value, and interpret the meaning, of the R Square.
| Income | Debt |
| 319000 | 458000 |
| 71000 | 153000 |
| 33000 | 0 |
| 104000 | 98000 |
| 45000 | 83000 |
| 6000 | 13000 |
| 43000 | 50000 |
| 165000 | 200000 |
| 37000 | 40000 |
| 167000 | 270000 |
| 79000 | 110000 |
| 18000 | 13000 |
| 43000 | 65000 |
| 26000 | 35000 |
| 75000 | 108000 |
| 185000 | 283000 |
| 24000 | 13000 |
| 20000 | 33000 |
| 33000 | 80000 |
| 43000 | 40000 |
| 2000 | 0 |
| 124000 | 145000 |
| 85000 | 125000 |
| 0 | 0 |
| 126000 | 128000 |
| 6000 | 0 |
| 118000 | 28000 |
| 87000 | 125000 |
| 142000 | 128000 |
| 90000 | 80000 |
| 83000 | 125000 |
| 18000 | 35000 |
| 0 | 0 |
| 94000 | 153000 |
| 153000 | 245000 |
| 122000 | 28000 |
| 73000 | 100000 |
| 14000 | 3000 |
| 43000 | 18000 |
| 175000 | 200000 |
| 138000 | 135000 |
| 33000 | 70000 |
| 81000 | 40000 |
| 43000 | 50000 |
| 10000 | 23000 |
| 96000 | 123000 |
| 128000 | 190000 |
| 92000 | 148000 |
| 206000 | 350000 |
| 79000 | 143000 |
| 92000 | 155000 |
| 18000 | 23000 |
| 4000 | 8000 |
| 4000 | 0 |
| 171000 | 235000 |
| 149000 | 185000 |
| 128000 | 163000 |
| 118000 | 188000 |
| 10000 | 10000 |
| 22000 | 13000 |
| 81000 | 123000 |
| 187000 | 295000 |
| 201000 | 255000 |
| 81000 | 75000 |
| 18000 | 5000 |
| 6000 | 28000 |
| 45000 | 53000 |
| 293000 | 355000 |
| 41000 | 93000 |
| 31000 | 13000 |
| 85000 | 88000 |
| 16000 | 35000 |
| 75000 | 103000 |
| 238000 | 320000 |
| 120000 | 123000 |
| 212000 | 163000 |
| 67000 | 108000 |
| 212000 | 265000 |
| 18000 | 30000 |
| 193000 | 243000 |
| 126000 | 135000 |
| 128000 | 168000 |
| 8000 | 23000 |
| 57000 | 43000 |
| 146000 | 208000 |
| 106000 | 190000 |
| 63000 | 120000 |
| 71000 | 133000 |
| 214000 | 260000 |
| 71000 | 105000 |
| 193000 | 385000 |
| 201000 | 275000 |
| 102000 | 113000 |
| 18000 | 33000 |
| 71000 | 123000 |
| 169000 | 258000 |
| 87000 | 100000 |
| 61000 | 98000 |
| 96000 | 118000 |
| 228000 | 288000 |
| 79000 | 90000 |
| 12000 | 10000 |
| 191000 | 210000 |
| 0 | 0 |
| 8000 | 13000 |
| 18000 | 0 |
| 124000 | 158000 |
| 134000 | 210000 |
| 85000 | 123000 |
| 122000 | 155000 |
| 155000 | 178000 |
| 0 | 0 |
| 214000 | 238000 |
| 124000 | 88000 |
| 53000 | 80000 |
| 26000 | 30000 |
| 14000 | 20000 |
| 26000 | 28000 |
| 4000 | 0 |
| 126000 | 70000 |
| 49000 | 58000 |
| 20000 | 30000 |
| 81000 | 43000 |
| 55000 | 108000 |
| 33000 | 30000 |
| 61000 | 60000 |
| 120000 | 140000 |
| 110000 | 128000 |
| 90000 | 55000 |
| 61000 | 95000 |
| 47000 | 78000 |
| 33000 | 60000 |
| 71000 | 143000 |
| 41000 | 63000 |
| 85000 | 105000 |
| 159000 | 148000 |
| 53000 | 13000 |
| 100000 | 180000 |
| 63000 | 73000 |
| 79000 | 98000 |
| 85000 | 78000 |
| 55000 | 95000 |
| 6000 | 8000 |
| 136000 | 140000 |
| 14000 | 20000 |
| 26000 | 45000 |
| 132000 | 190000 |
| 116000 | 115000 |
| 108000 | 150000 |
| 41000 | 45000 |
| 6000 | 43000 |
| 4000 | 15000 |
| 94000 | 133000 |
| 47000 | 5000 |
| 100000 | 90000 |
| 6000 | 10000 |
| 67000 | 118000 |
| 47000 | 98000 |
| 291000 | 333000 |
| 128000 | 163000 |
| 8000 | 10000 |
| 24000 | 30000 |
| 98000 | 93000 |
| 2000 | 5000 |
| 33000 | 50000 |
| 51000 | 58000 |
| 39000 | 40000 |
| 49000 | 80000 |
| 31000 | 23000 |
| 195000 | 270000 |
| 6000 | 15000 |
| 69000 | 65000 |
| 26000 | 30000 |
| 4000 | 0 |
| 126000 | 145000 |
| 132000 | 183000 |
| 159000 | 293000 |
| 277000 | 358000 |
| 120000 | 93000 |
| 67000 | 120000 |
| 10000 | 33000 |
| 157000 | 205000 |
| 142000 | 140000 |
| 69000 | 90000 |
| 100000 | 55000 |
| 191000 | 200000 |
| 20000 | 33000 |
| 132000 | 165000 |
| 18000 | 25000 |
| 2000 | 0 |
| 37000 | 30000 |
| 112000 | 143000 |
| 210000 | 280000 |
| 22000 | 23000 |
| 0 | 0 |
| 108000 | 120000 |
| 28000 | 23000 |
| 104000 | 243000 |
| 63000 | 73000 |
| 120000 | 133000 |
| 151000 | 175000 |
| 35000 | 73000 |
| 63000 | 80000 |
| 39000 | 48000 |
| 85000 | 118000 |
| 108000 | 158000 |
| 92000 | 73000 |
| 85000 | 90000 |
| 6000 | 8000 |
| 22000 | 40000 |
| 63000 | 50000 |
| 59000 | 58000 |
| 79000 | 150000 |
| 163000 | 200000 |
| 20000 | 28000 |
| 134000 | 168000 |
| 12000 | 0 |
| 12000 | 10000 |
| 126000 | 155000 |
| 10000 | 18000 |
| 12000 | 5000 |
| 114000 | 113000 |
| 120000 | 120000 |
| 39000 | 48000 |
| 126000 | 105000 |
| 171000 | 213000 |
| 155000 | 183000 |
| 83000 | 133000 |
| 291000 | 355000 |
| 102000 | 113000 |
| 106000 | 98000 |
| 75000 | 135000 |
| 87000 | 133000 |
| 79000 | 95000 |
| 110000 | 110000 |
| 31000 | 43000 |
| 22000 | 35000 |
| 2000 | 5000 |
| 73000 | 118000 |
| 0 | 0 |
| 128000 | 243000 |
| 210000 | 228000 |
| 33000 | 50000 |
| 49000 | 55000 |
| 8000 | 15000 |
| 116000 | 175000 |
| 59000 | 120000 |
| 79000 | 98000 |
| 33000 | 60000 |
| 90000 | 110000 |
| 45000 | 78000 |
| 128000 | 160000 |
| 130000 | 170000 |
| 65000 | 103000 |
| 26000 | 38000 |
| 35000 | 50000 |
| 130000 | 160000 |
| 0 | 0 |
| 71000 | 95000 |
| 43000 | 68000 |
| 110000 | 115000 |
| 185000 | 320000 |
| 69000 | 83000 |
| 67000 | 100000 |
| 104000 | 165000 |
| 102000 | 80000 |
| 120000 | 118000 |
| 53000 | 60000 |
| 10000 | 13000 |
| 55000 | 85000 |
| 73000 | 140000 |
| 57000 | 73000 |
| 67000 | 95000 |
| 53000 | 63000 |
| 6000 | 20000 |
| 120000 | 118000 |
| 112000 | 158000 |
| 153000 | 193000 |
| 53000 | 48000 |
| 14000 | 18000 |
| 81000 | 13000 |
| 110000 | 130000 |
| 167000 | 250000 |
| 39000 | 55000 |
| 43000 | 60000 |
| 199000 | 185000 |
| 33000 | 30000 |
| 87000 | 73000 |
| 45000 | 60000 |
| 214000 | 258000 |
| 37000 | 33000 |
| 85000 | 113000 |
| 73000 | 123000 |
| 177000 | 200000 |
| 49000 | 70000 |
| 120000 | 180000 |
| 53000 | 73000 |
| 102000 | 70000 |
| 31000 | 55000 |
| 43000 | 33000 |