A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = β0 + β1x + ε where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data was collected from rush hour for 6 different highways in the city.  Traffic Flow (y) Vehicle Speed (x) 1,254 35 1,327 40 1,227 30 1,335 45 1,348 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2   1. Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) 2. Find the value of test statitc and p-value.   3. Based on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.5 8.4 6.9 3.9 2.7 2.8 2.2 0.6 yy 13.7 11 10 7 6.3 6.4 6.2 4.8 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.82x+4.16.y=0.82x+4.16. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.7 thousand automatic weapons?Answer = Round to 3 decimal places.

Data from the US Department of Energy’s US Energy Information Administration (eia.doe.gov) provides a look at the energy-related carbon dioxide emissions by end use sector (residential, commercial, industrial, transportation) from years 1990 to 2009. (Report # DOE/EIA0573(2009)). Here we would like to see if the CO2 emissions from the Industrial sector are less than that from the Transportation sector. Below are the results: 14. What type of study is this? a. Paired b. Two-Sample Independent 15. What type of plot would we use? a. Histogram of the differences b. Side-by-side boxplots c. Pie chart d. Bar graph 16. Was the HOV/pooled test used above (hint: look at the df)? YES NO 17.  Is there evidence that the CO2 emissions from the Industrial sector are less than that from the Transportation sector? YES NO 18. If we were to test to see if there was a difference between the CO2 emissions from the Industrial sector and the Transportation sector, what would be the p-value? (report to 3…

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.5 8.5 7 3.7 2.7 2.5 2.6 0.8 yy 13.8 11.1 10.1 7.2 6.4 6.1 6.1 4.8 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation ˆy=0.85x+4.05.y^=0.85x+4.05. Use this equation to answer the following.A) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons?Answer =  Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.3 thousand automatic weapons?Answer =  Round to 3 decimal places.

You are asked to determine whether laptop brand A charges a higher premium for its laptops than brand B. You observe a sample of six laptops, their prices and brand. You observe a performance benchmark x for each of the laptops. Let (yi, xi) denote the price and performance of laptop i. Your data are: Obs. i=1 i = 2 i = 3 i = 4 i = 5 i = 6 Brand Price A $1000 A $1500 A B B B $2000 $1500 $2000 $2500 Performance 1 2 3 3 4 5 Draw a scatter plot of price vs. performance. Which brand produces more expensive laptops on average in the sample? Would you say this brand charges a higher premium? Explain by writing down an appropriate regression model, estimation results and an intepretation of your results. If you omit brand information from your regression and just regress price on performance, are you likely to over or under-estimate the association between performance and price? Explain by determining the likely sign of the omitted variables bias as in lecture and comparing it with the…

7.55 The following variables were recorded for several counties in Minnesota in 1977: y = average rent paid per acre of land with alfalfa X₁ = - average rent paid per acre for all land x₂ = average number of dairy cows per square mile x3 = proportion of farmland in pasture The data for 34 counties are given in Table 7.5 (Weisberg 1985, p. 162). Can rent for alfalfa land be predicted from the other three variables? (a) Find 3 and ². (b) Find , and ß using Sex and sx as in (7.46) and (7.47). (c) Find R² and R2.

;AUTO . Complete the following table and calculate the correlation coefficient, regression equation, and coefficient of determination, R Sunlight hours, x Section IV- Regression & Correlation y ху Yield (flowers), y 0.3 11 0.6 18 0.9 29 1.2 33 1.5 43 Σ Σ a. Correlation coefficient, r- b. Write down the regression equation: c. Use the regression equation to predict the flower yield if the amount of sunlight is 1.1 hours.. Cancel Done 中。

Imagine that there is a correlation of r = 0.65 between variable X and variable Y.  Based on the correlation between these two variables (and only these two variables), what is a person's predicted value on variable Y, when his X value on variable X is a z score of 1.5?  Please provide your answer as a z score with a minimum of three decimal places.

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.

A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables?     A positive linear relationship (r close to 1)     A positive linear relationship (r close to -1)     A negative linear relationship (r close to 1)     A negative linear relationship (r close to -1)…