4, Correlation and Regression (Due by April 17) PSY 381, 2017 Spring 1. The state of Vermont is divided into 10 Health Planning Districts, which correspond roughly to counties. The following data for 1980 represent the percentage of births of babies under 2500 grams (y), the fertility rate for females younger than 18 or older than 34 years of age (x1), and percentage of births to unmarried mothers (x2), for each district. District X1 X2 Y 1 43.0 9.2 6.1 2 55.3 12.0 7.1 3 48.5 10.4 7.4 4 38.8 9.8 6.3 5 46.2 9.8 6.5 6 39.9 7.7 5.7 7 43.1 10.9 6.6 8 48.5 9.5 8.2 9 40.0 11.6 6.3 10 56.7 11.6 6.9 (a) make a scatter diagram of Y and X1 (b) Calculate the correlation between Y and X1 (c) Calculate the correlation between Y and X2 (d) Use t-test to measure if the correlations are significant for exercise (c) and (d) (e) Use z-test to measure if these two correlation are different from each other 2. The following data represent the actual heights and weights referred for a group of college students. a. Using SPSS to find out \"a- the intercept\" and \"b- the slope\" and write the regression equation of weight predicted from height for these data. Interpret the slope and the intercept b. What is the correlation coefficient for these data? c. Are the correlation coefficient (r) and the slope (b) significant different from zero? d. Using your own height and the equation above to predict your own weight. e. How much is your actual weight greater than or less than your predicted weight? (If you don't feel comfortable with your own height and weight, you can use mine: height: 64, weight 140 Height Weight Height Weight Height Weight Height Weight 70 150 73.5 160 68 140 67 150 60 140 69 155 74 180 69 155 72 180 73 165 66 135 70 155 75 190 72 150 71 170 72 215 68 145 74 190 58 105 67 143 69 150 72 195 70 130 69 145 59.5 115 71 138 75 185 73 155 71 140 74 160 64 140 71 150 72 142 72 155 71 155 68 155 63 116 70 153 63 135 62 138 65 125 67 145 70 155 73 166 72 175 71 170 72 215 75 160