Determine whether the following is true or false: In a multiple linear regression, y = ẞ₁ + ẞ₁x, + ẞ₂×₂ + u, 0 if corr(x,, x) = 1, then ẞ, cannot be estimated, because the numerator in the formula for ß, is zero. Explain your answer in two sentences or fewer.

Choose all correct answers regarding assumptions for B₁ in a simple linear regression. (a) If there is no variation in X, we cannot identify the estimate of ẞ₁, so E[ẞ₁] = ẞ, does not hold. (b) It measures the y-intercept of the estimated regression line. (c) As the sample size increases, ẞ₁ is more likely to be closer to ẞ, assuming E[ß₁] = ß₁. (d) If the sample covariance between x and y is positive, then B₁ > 0.

Choose all correct answers regarding the multiple linear regression model: y = Bo+ B₁x₁ + B2X2 + + BkXk + U. (a) If you add a relevant variable XK+1, but corr(XK, Xk+1) is high, then you must not include xk+1 in the regression equation. (b) Adding a variable XK+₁ may lower the R² value. (c) Adding all the variables in the dataset does not imply that E[u | X1, X2, ... Xk] = 0. (d) We can estimate the value of ẞ₁ by minimizing Σ(û¡)².

Refer to the Stata output from an analysis of data on Store sales. The data include nominal store-level sales (measured in for the month of June 1996 from 844 stores of a national retail chain. The other variables are: A categorical string variable loctype which indicates the type of store location and takes one of three values: "mall" = 1 if the store is located in a shopping mall (indoor or outdoor) "street" = 1 if the store is located on a street "strip" = 1 if the store is located on a strip or highway ⚫ medhhinc = the median household income of the city where the store is located, measured in $1,000 • empl = the total number of employees working in the store in June 1996 . sqft = the store's size, measured in 1,000 square feet A manager wants to know how average monthly sales varies with the characteristics of a store and its location and uses Stata to perform the regression analysis shown. gen sqftXmedhhinc =sqft*medhhinc . reg sales mall street medhhinc empl sqft sqftXmedhhinc,…

We would like to examine whether there is a differential effect of study hours on test scores between students whose first language is English and those whose first language is not English by adding an interaction term. gen hoursEng = study_hours *English . reg test_score study_hours English hoursEng Source SS df MS Number of obs 876 Model Residual 136565.839 18952.9115 3 45521.9464 872 21.7349902 F(3, 872) Prob F 2094.41 0.0000 R-squared 0.8781 Total 155518.751 875 177.735715 Adj R-squared = Root MSE 0.8777 = 4.6621 test_score Coef. Std. Err. t P>|t| [95% Conf. Interval] study_hours English hoursEng 1.82049 .0369748 49.24 0.000 8.318905 .8108202 10.26 0.000 .101876 cons 43.52037 .0516819 .5767457 1.97 75.46 0.049 0.000 1.74792 6.727517 .0004404 42.3884 1.89306 9.910292 .2033115 44.65234 (a): What is the predicted test score for an individual who studied two hours and whose first language is not English? (Round to two decimal places) (b): Choose all correct answers (a) The differential…

Determine whether the following statement is true or false. Suppose you reject the null hypothesis: Ho: ẞ₁ = ẞ₂ = 0. Then, both ẞ₁ = 0 and ẞ2 ± 0. Explain your answer in two sentences or fewer.

Choose one correct answer: The ---A----- dataset includes 100,000 students from 512 schools observed over 12 months. To control differences between schools and months, we should add a total of What are A and B? (a) A: Time series, B: 524 (b) A: Time series, B: 522 (c) A: Panel, B: 524 (d) A: Panel, B: 522 dummies.

Refer to the Stata output from an analysis of data on Store sales. The data include nominal store-level sales (measured in for the month of June 1996 from 844 stores of a national retail chain. The other variables are: A categorical string variable loctype which indicates the type of store location and takes one of three values: "mall" = 1 if the store is located in a shopping mall (indoor or outdoor) "street" = 1 if the store is located on a street "strip" = 1 if the store is located on a strip or highway ⚫ medhhinc = the median household income of the city where the store is located, measured in $1,000 • empl = the total number of employees working in the store in June 1996 . sqft = the store's size, measured in 1,000 square feet A manager wants to know how average monthly sales varies with the characteristics of a store and its location and uses Stata to perform the regression analysis shown. gen sqftXmedhhinc =sqft*medhhinc . reg sales mall street medhhinc empl sqft sqftXmedhhinc,…

Essay question. In this regression analysis, you are interested in the effect of age on the amount of gasoline used by a car, measured in gallons. Suppose you analyze your dataset and find the following results. Based on the Stata output, how can you improve the analysis? State 3 issues in the figure and table, and possible solution for each problem you can apply based on what you have learned in class. gasoline_use 40 20 100 .reg gasoline_use age Source SS df MS Model Residual 28.1117271 9969.5248 1 28.1117271 23 433.4576 Number of obs F(1, 23) Prob > F R-squared 25 0.06 0.8012 0.0028 a Total 9997.63653 24 416.568189 Adj R-squared Root MSE -0.0405 20.82 gasoline_use Coef. Std. Err. t P>|t| [95% Conf. Interval] age cons -.0688645 .2704114 62.37748 13.86839 -0.25 0.801 4.50 0.000 -.6282532 .4905242 33.68853 91.06643 20 40 60 80 age