Correlation & Regression This week we learned two ways to describe a relationship between numerical variables: correlation and regression. In this exercise, you will choose two possible explanatory variables from a data set, and determine whether they are significantly correlated with the response variable. You have 2 data sets to pick from: . Data set 1 Response variable: baby's birthweight o Other variables: mother's age, # of cigarettes smoked daily by mother, mother's height, length of gestation, father's age, father's height, and # of cigarettes smoked daily by father . Data set 2 Response variable: crime rate o Other variables: proportion of young males in population, expenditure on police, proportion of males vs females in population, youth unemployment, mature unemployment, median wage E.g. If I choose data set 1, I may choose to explore mother's age and father's age. I will compare mother's age to birthweight, and I will compare father's age to birthweight to see if either or both variables have a correlation with the baby's birthweight.Steps 1. Choose your data set 2. Choose 2 variables from the "other" list. 3. For each "other" variable you choose a. Create a scatterplot with the response variable (recommended tools: Desmos, Excel, Google Sheets) b. Find its correlation with the response variable (r) 4. If r > 0.1, test the significance of the correlation with a t-test a. State your null and alternative hypotheses i. Ho - there is no correlation between variables p = 0 ii. Ha - there is correlation between variables p # 0 b. The calculations for tcalculated c. Your tcritical d. A conclusion Data Source: https://www.sheffield.ac.uk/mash/statistics/datasets& Y - 100% * @ View only - A1 fx Birthweight Father's Daily Mother's Daily Mother Father's Age Num of Cig Father's Height Height Birthweight Gestation Mother's Age Num of Cig 179 20 U 162 23 35 4.55 44 19 0 183 171 4.32 40 19 31 25 185 41 35 172 174 26 25 189 4.07 44 20 42 175 30 0 184 3.94 24 31 180 3.93 38 29 165 173 40 24 157 31 3.77 21 165 21 25 185 3.65 42 172 20 7 172 10 3.63 38 18 22 179 38 20 157 0 3.42 37 170 12 .35 41 27 29 181 13 .27 40 24 16 31 35 183 14 38 25 41 15 25 183 21 29 30 25 182 40 28 158 39 171 37 27 178 39 27 162 25 25 175 34 26 23 193 N 39 19 165 169 2.65 33 24 149 26 170 24 12 185 40 20 24 12 176 .14 41 22 160 20 183 78 37 19 165 25 200 25 2.51 39 22 159 23 185 37 20 163 20 35 159 166 37 25 173 27 .05 35 41 180 161 20 35 .92 33 20 180 41 32 12 173 38 25 57 41 50 191 40 163 .59 31 12 12 152 37 25 170 21 3.3 40 27 180 38 30 12 165 38 50 22 157 32 25 169 3.32 39 23 17 179 39 21 17 156 24 7 2 74 0 183 45 28 25 163 30 35 178 30 170 50 25 40 36 86 39 25 161 46 0 175 27 55 41 37 25 170 30 25 181 153 40 26 181 39 23 25 181 23 2 3.41 31 25 162 32 50 194 40 3.18 38 31 25 185 35 163 41 19 41 27 50 186 42 35 20 35 170 23 168 31 0 173 50 43 2.75