1 Is the relation between Y and X statistically significant Why or why not P value is 41 which is 41 a will only ever be 1 5 or 10 Therefore P is definitely greater than a There is NO RELATIONSHIP because PV a do not reject 2 The following tables show the result of regreesion between X and Y First fill out the marked cells yellow cells with question mark and then answer the following questions a Find R2 and explain what it means SSR SST 2546 58 10477 6 24 SST SSR 10477 6 2546 58 7931 01 b Find the SSE c Find the SST d Find the SSR 10477 6 2546 58 e Find MSE 610 07 f Find F statistic MSR MSE 2546 58 1 610 07 4 17 g Find the degree of freedom for SSE SST and SSR DF for SSE 13 DF for SST 14 DF for SSR 1 h Find the intercept b0 and interpret it 11 39 when X is 0 Y in average 11 39 i Find the slope b1 and interpret it 2 61 how much Y changes when X increase by 1 unit j Write down the null and alternative hypothesis for the intercept and slope H0 B1 0 H1 B1 0 o B is ALWAYS uppercase k Are intercept and slope statistically significant Why or why not P value 06 6 If a 10 relation reject H0 B1 0 because P 6 would be less than a 10 If a 10 NO relation do NOT reject H0 l What is your conclusion about the regression line or relationship between Y and X based on the results of hypothesis tests m Write down the estimated regression line Y 11 39 2 61X1 n The range of X is from 8 to 25 What is the predicted value for Y if X is equal to 6 Y 11 39 2 61 6 27 07 can t use it because 6 isn t in the 8 to 25 range o The range of X is from 8 to 25 What is the predicted value for Y if X is equal to 10 Y 11 39 2 61 10 37 49 can use it because 10 is in the 8 to 25 range 3 4 5 6 Example SST SSR SSE 10 15 5 Not possible because sum of squares can t be negative SST is always bigger than 0 You need b1 to calculate b0 b0 14 5 b1 2 229 SSE 23571 52 14 5 582 2 229 6727 6 97 86 SSR 14 5 582 2 229 6727 6 17 731 81 SST 97 86 731 81 837 53 874 87 4 Example 1 2 2 2 3 2 14 1 2 3 2 39 b1 will be given B1 0 10 19 Y 096 849X1 64X2 b1 if X1 goes up by one unit when X2 is constant X goes up by 849 units b2 if X2 goes up by one unit when X1 is constant X goes up by 64 units MSR 60 2 30 MSE 120 8 6 67 30 6 67 4 5 F 4 5 F with a 05 2 DF top 18 DF left F table 3 55 H0 B1 B1 0 H1 B1 0 or B2 0 F critical value of F Reject H0 relationship between X1 and X2 R2 SSR SST 60 180 3333 33 33