(a) Let H = (h₁, h2, ..., hy). What is the dimensionality of this matrix? (b) Define a matrix S whose entries are: (S)i,j = hihj ||hi|| ||hj||, You observe that this matrix seems to have a "blocky" structure where the bottom right quarter of the matrix has notably large values, close to 1. What might this indicate about the users? Use at most 3 sentences, appealing to linear algebraic concepts.

The maintenance manager at a trucking company wants to build a regression model to forecast the time (in years) until the first engine overhaul based on four predictor variables: (1) annual miles driven (in 1,000s of miles), (2) average load weight (in tons), (3) average driving speed (in mph), and (4) oil change interval (in 1,000s of miles). Based on driver logs and onboard computers, data have been obtained for a sample of 25 trucks. A portion of the data is shown in the accompanying table. Time Miles Load Speed Oil 7.7 42.9 22.0 44.0 16.0 0.8 98.3 20.0 47.0 34.0 6.3 61.1 22.0 62.0 15.0 E Click here for the Excel Data File b. Estimate the regression model. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Time = Miles Load Speed oil + + d. What is the predicted time before the first engine overhaul for a particular truck driven 60,000 miles per year with an average load of 25 tons, an average driving speed of 53 mph, and 21,000 miles…

Find the equation y = ẞo + B₁x of the least-squares line that best fits the given data points. (3,6), (4,4), (6,2), (7,0)

The marketing research department of a large company knows that the company's monthly sales are influenced by the way in which it spends money on marketing. For example, monthly expenditures such as the ones listed below are known to have an effect on y, the company's total monthly sales (in millions of dollars). X1 = money spent on television advertising (in 1000's of dollars) X2 money spent on promotion (i.e., free samples) X3 = money spent on newspaper advertising (in 1000's of dollars) X4 average discounts offered to retail outlets (in %) Using data from the previous 18 months, the company decides to collect data on 6 of the independent variables to use in a multiple regression model for estimating monthly sales. If the R´ for this model is 0.93, fill in the missing entries in the ANOVA table associated with this model. Do all calculations to at least three decimal places.

The variance of temperatures (Fahrenheit) in Denver, Colo. is 328.87. What is this variance if temp is re-expressed in Celsius?  [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]

The line of best fit through a set of data isy=46.539+4.023xy=46.539+4.023xAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 40?y =  Round to 1 decimal place.

use calculator method

This dataset continues our saga of modeling the price of this popular Honda automobile. The dataset has now been cleaned to remove the columns with the dealership where the car was offered for sale and specific trim. (a) write out your model in econometric notation. Be very precise!  (b) using the 93 observations in the dataset, estimate a model where price is a function of age, mileage and trim of the car. Be sure to avoid the dummy variable trap!! Fully report the results of your model. In this case, interpretation of the coefficients on the dummy variables is particularly important.  (c) test the hypothesis that the specific trim does not affect the price of a Civic. Be sure to do all parts of the hypothesis test.  (please fully describe steps if you are using Excel)  Price Years Old KM EX EXT SE Sport Touring 6555 9 290363 0 0 0 0 0 9999 9 142258 0 0 0 0 0 10281 6 132644 0 0 0 0 0 12480 5 167125 0 0 0 0 0 12991 7 57398 0 0 0 0 0 12991 6 93046 0 0 0 0 0 12991…

The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y)   6.22 −0.08   8.01   0.25   8.67 −0.14 10.61   0.00 12.5   0.08 11.94   0.03 12.55 −0.07 17.93   0.29 18.34   0.23…

You were asked to help with analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time. The aim of the analysis is to see whether the birth weights of the infants are associated with mothers AGE at birth (continuous variable in years) and mothers smoking status (the maternal smoking status MSS contains 4 categories “Non-smoker”, “Past-smoker”, “Passive-smoker”, “Smoker”) and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”). Questions: 1.Write down the population model that estimates BW based on variables AGE and BOROUGH(with the dummy variables). Make sure that it is clear what each predictor means. 2.How many parallel lines are computed by model from population model you created above? 3.Write down the population model that estimates BW based on variables AGE, MSS(with their dummy variables) and BOROUGH(with their dummy variables). Also write down the number of parrallel lines.…