Decide if a linear model is reasonable and describe the coefficient of determination
Students in an introductory statistics class at The University of Queensland participated in a simple experiment.
The students are interested in building a model that can be used to estimate a student’s weight based on the student’s height.
Data Set
Height Weight
173 57
179 58
167 62
195 84
173 64
184 74
162 57
169 55
164 56
168 60
170 75
178 58
170 68
187 59
180 72
185 110
170 56
180 70
166 56
155 50
175 60
140 50
163 55
182 75
176 59
177 74
170 60
172 60
189 60
178 56
175 75
180 85
160 57
164 66
175 65
163 55
185 90
169 68
165 63
155 49
175 66
178 63
184 65
170 60
162 60
164 46
171 70
182 85
174 60
167 70
157 41
183 73
167 75
171 67
182 63
173 70
182 85
158 51
160 49
180 75
180 77
188 87
164 54
180 102
178 62
166 50
175 57
180 80
182 98
151 42
186 87
190 82
179 80
165 48
172 53
173 64
170 53.5
170 58.5
163 51
191 78
172 59
171 71
180 76
194 110
167 63
192 105
194 95
189 88
162 50
175 54
175 78.5
186 96
178 86
170 58
165 58
164 78
180 65
170 62
155 55
165 60
168 55
68 63
170 63
179 80
163 47
93 27
161 43
182 60
170 65
185 85
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The coefficient of determination ([latex]R^2[/latex]) is a measure of the proportion of the variation of a response variable in linearly related bivariate data that can be explained by its relationship with the explanatory variable.