Question

Question 3 (10pts) As part of a research program for a new cholesterol drug, a pharmaceutical company would like to investigate the relationship between the ages and LDL (low-density lipoprotein) cholesterol of men. The accompanying data set shows the ages and LDL cholesterol levels of seven randomly selected men. Construct a 95% prediction interval to estimate the LDL cholesterol level of a 29-year-old man. Age 22 38 Cholesterol 144 175 160 200 160 25 32 43 32 141 42 210 Determine the upper and lower limits of the prediction interval. (Round to one decimal place as needed.)

please show all the work. if you use excel please show the screenshots. Thank you !

Answer 1

Y x 144 175 160 20 38 25 za 43 32 42 Y? xili 484 20736 3168 1444 130625 16650 625 25600 400 1024 40000 16400 1849 25600 16880 11024 119881 us12 [1764 44100 8820 Sun Sun huna 8214 206542 40430 160 141 216 suma 1190 sun 2234 SSxx 2 121 Ssyy? si SSxy= =(2x)", 8214 - 0234 3913143 2 - 1 1 2 2 2 2 2 2065 206542 - 4 11190 2 4242 Exivi Lixos) (EY) 340430 -3 (234) (190)= 650 2 1.6594 Por @ *X) 14.52915 Regression equation in 2 114.5295 +1.65948 Plugging x 29, 2 114.5295 + (1.6594x29), 162.6513 2 SSXY SSxx .. (2 Ssyy? 2 1078.5923 Å Ssxy 2 SS Regression 2 + SS Error 42 42.2 SS Total . Regrunnion sum of squares - SS Regrana We know that, SS Total SS Error 2-(10 78.8923 - 4242) - 3 163.4077 3163.4077 . Mean squared error's, MSE 2 SS Error n-2 2 7-2 2 632.6815 225. 1532 Standard enor + SSxx E 2 tal2,m-2 391-7143 8. UMSE Margin error of prediction centerval 22 ( 14 h 2 2.571x 632.6815 (1+5+ (22,-33.428613 2 68.7798 Hence, 957 prediction internal for ŷ 2 162.6513, isa P.I2 (16216513 -& 162.6513 +6 193.8715,231.4312 lower limit 293.91 upper limit a 231.4 13 +€) 2