Need help with some simple linear regression problem that compares height ans shoe size

height shoe_size

188 44

172 42.5

171 39

167 38

165 38

165 37

160 37

167 36

178 43

171 42

165 37

173 39

157 35

160 38

177 42

168 38

175 42

170 39

166 39

153 37

174 42

181 43

160 36

182 44

161 36

165 37

181 44

160 35

160 36

163 36

173 42

161 38

177 42

161 37.5

160 36

181 46

154 36

173 39

163 36

168 37

167 40

159 37

165 40

163 37

175 40

160 36

165 38

158 36

165 36

170 42

169 38.5

169 38

182 42

160 37

189 44

160 38

179 44.5

177 40

177 43

165 36

172 37

172 42.5

164 37

188 45

165 38

170 42

175 42

173 42.5

185 44

174 42

158 36

164.5 38

158 36

163 37.5

163 36

175 41

162 37

177 42

175 39

171 39

173 42

163 36

164 38

168 38

168 36

168 37

178 41

158 36

168 37

170 40

168 43

187 44

170 44

165 39

175 42

168 38

168 39

160 37

156 36.5

170 38

186 44

162 37

158 36

180 44

165 36

178 42

165 37

170 45

183 44.5

170 39

A sample size of 110 is taken from students enrolled in ECON7300 in semester 2, 2019 to study the relationship between their height and shoe size. The variables in the dataset are: height (Y, in cm) . shoe_size (X, in number) The dependent variable for your analysis is height. Answer the following questions using Dataset 3. (a) Estimate a regression model using X to predict Y (state the simple linear regression equation). (b) Interpret the meaning of the slope. (c) Predict Y when X = 43.5 (d) Compute the coefficient of determination and interpret its meaning. (e) Compute the standard error of the estimate and interpret its meaning. Judge the magnitude of the standard error of the estimate. (f) Perform a residual analysis (plot the residuals) and evaluate whether the assumptions of regression have been violated. (g) Test for the slope using t test (follow all the necessary steps). Assume 5% level of significance. (h) Test for the slope using F test (follow all the necessary steps). Assume 5% level of significance. (i) Test for the correlation coefficient (follow all the necessary steps). Assume 5% level of significance. (j) Compute a 95% confidence interval estimate of the mean Y for all students enrolled in ECON7300 in semester 1, 2019 when X = 43.5 and interpret its meaning. (k) Compute a 95% prediction interval of Y for a student enrolled in ECON7300 in semester 1, 2019 when X = 43.5 and interpret its meaning