Question 6 1 pts Consider the following multiple linear regression model Y: 50 +151X1 +2X2+- - -+5po + E Which of the following is TRUE of the least squares {LS} regression line for this model? C) The sum of residuals is always zero. 0 lfwe can reject the null hypothesis H.) : 51 = 0 at the 95% condence level, then we are 95% condent that there is a causal relationship between X1 and Y . Q There may be a linear relationship between X] , X2, . . . , Xi, and the residuals of the least squares line. C) All of the above. 0 None of the above. Question 7 1 pts In the 1994 lm "Pulp Fiction", Vincent Vega was appalled that a milkshake cost $5 which, adjusting for ination, roughly equals to $9.50 today. Assume that in 2022, milkshake prices follow a normal distribution with mean $5.50 and standard deviation $2. What is the probability of seeing a milkshake that costs at least $9.50? 0 0.025 O 0.005 O 0.16 O 0.05 Question 8 1 pts In the simple regression model setting, o is the standard deviation of the error term c. Assuming nothing else changes, which of the following statements is TRUE? O The smaller the value of o, the more accurate our predictions will be. O o will get smaller as the sample size gets larger. O The larger the slope coefficient, the more accurate our predictions will be. O o will be smaller for regressions with steeper true slope coefficients. O None of the above. Question 9 1 pts In a recent Gallup poll of 1203 adults, 68% reported being "very satisfied" with the rollout of the US vaccination process (up 24% from the last poll conducted in February). Report a 95% confidence interval for the true proportion of adults that are "very satisfied". O (0.65, 0.71) O (0.60, 0.76) O (0.68, 0.84) O (0.52, 0.68) O Cannot be determined from the information given