Consider the Simple Linear Model that predicts housing prices based on square feet. Can you think of another variable you can add that would extend this model. How about bed rooms? Multiple regression. Regression between one dependent variable and two or more independent variables square feet 1300 1700 1900 2400 2250 1600 2700 4000 Bed Rooms 2 2 2 3 3 3 4 4 Price in kilo dollars 180 195 200 240 260 225 300 400 1. What is the meaning of the central limit theorem for means, and the central limit theorem for proportions? When and how are they used? Compare and contrast the central limit theorem for means vs. the central limit theorem for proportions. Include at least one similarity. and one difference. Explain the differences in the sampling distributions of x for large and small samples under the following assumptions. Complete parts a and b. a The variable of interest, x, is normally distributed. Choose the correct answer below. OA. There are no differences, as both large and small samples will have normal sampling distributions. 8. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but large samples will not have a sampling distribution. OC. Large samples will have a normal sampling distribution due to the Central Limit Theorem, but small samples will not have a normal sampling distribution. OD. There are no differences, as neither large nor small samples will have normal sampling distributions. b. Nothing is known about the distribution of the variable x. Choose the correct answer below. OA Large samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of small samples is unknown. OB. Small samples will have a normal sampling distribution due to the Central Limit Theorem, but the sampling distribution of the large samples is unknown. OC. There are no differences, as both large and small samples will have normal sampling distributions. OD. There are no differences, as the sampling distributions for both large and small samples are unknown.