The following results were obtained from a regression of n = 14 housing prices (in dollars) on median family income, size of house, and size of lot: What is Mean Sum of df square F squares 4234 3 Regression SS: Residual SS: 3487 Total SS: Coefficient (b) Standard error(sb) VIF 0.34 1.3 Median family 1.57 income 11.2 2.9 Size of house (sq. ft) 23.4 Size of lot (sq. ft) -9.5 7.1 11.3 Constant 40,000 1000 (a) Fill in the blanks. (b) What is the value of ? (c) What is the standard error of the estimate? (d) Test the null hypothesis that R² = 0 by comparing the F-statistic from the table with its critical value. %3D (e) Are the coefficients in the direction you would hypothesize? If not, which coefficients are opposite in sign from what you would expect? (f) Find the t-statistics associated with each coefficient, and test the null hypotheses that the coefficients are equal to zero. Use a = 0.05, and be sure to give the critical value of t. %3D (g) What do you conclude from the variance inflation factors (VIFS)? What (if any) modifications would you recommend in light of the VIFS? (h) What is the predicted sales price of a house that is 1500 square feet, on a lot 60'x100', and in a neighborhood where the median family income is $40,000?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Answer only d, e, f
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