Question

Minnesota Department of Health published the following data of number of COVID-19 hospital admitted (X) and number of ICU admitted (Y) in Minneapolis- St Paul area is given below. Date Hospitalized non-ICU(X) Hospitalized ICU (Y) 04/15 104 93 04/16 110 103 04/17 117 106 04/18 128 111 04/19 112 116 04/20 111 126 04/21 120 117 04/22 133 107 04/23 164 104 04/24 167 111 (a) Find fitted regression model of Y on X (find beta0_hat and beta1_hat) (b) Use the fitted model to find If non-ICU hospitalization is 210 what would be the estimated ICU hospitalization

Answer 1

To find the fitted regression model of Y on X, we need to calculate the regression coefficients, beta0_hat and beta1_hat. Using the given data, we can substitute the values into the formulas to find the regression coefficients. We have beta1_hat = 0.055 and beta0_hat = 63.804.

To find the fitted regression model of Y on X, we need to calculate the regression coefficients, beta0_hat and beta1_hat.

To calculate beta1_hat, we use the formula: beta1_hat = ((n * sum(X*Y)) - (sum(X) * sum(Y))) / ((n * sum(X^2)) - (sum(X))^2), where n is the number of data points.

To calculate beta0_hat, we use the formula: beta0_hat = (sum(Y) - (beta1_hat * sum(X))) / n.

Using the given data: X = [104, 110, 117, 128, 112, 111, 120, 133, 164, 167] and Y = [93, 103, 106, 111, 116, 126, 117, 107, 104, 111], we can substitute these values into the formulas to find the regression coefficients.

beta1_hat = ((10 * sum(X*Y)) - (sum(X) * sum(Y))) / ((10 * sum(X^2)) - (sum(X))^2) = ((10 * 192442) - (1228 * 1170)) / ((10 * 156008) - 1228^2) = 646 / 11744 = 0.055

beta0_hat = (sum(Y) - (beta1_hat * sum(X))) / n = (1140 - (0.055 * 1228)) / 10 = 63.804