Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although ti medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet). 6.5 5.4 4.2 3.3 2.1 (units: mm Hg/10) 43.6 32.3 26.2 16.2 13.9 (units: mm Hg/10) Ex = 21.5, Ey = 132.2, Ex2 = 104.35, Ey² = 4086.34, Exy = 650.51, and r= 0.978. Ex 21.5 Ey 132.2 Ex2 104.35 Ey2 4086.34 Exy 650.51 r0.978 Use a 1% level of significance to test the claim that p > 0. (Use decimal places.) critical t

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…

When water flows across farmland, some soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow (liters per second) on the amount of soil (kilograms) washed away. The data are given in the following table:   Flow rate 0.31 0.85 1.26 2.47 3.75 Eroded soil 0.82 1.95 2.18 3.01 6.07           Let xx represent the flow rate variable and yy represent the variable for soil eroded. Then   \bar x = 1.73, s_x = 1.38, \bar y = 2.81, s_y = 1.99xˉ=1.73,sx​=1.38,yˉ​=2.81,sy​=1.99   Use this to complete the following calculation of the correlation coefficient for these data.   r = \frac{1}{n-1}\left[\left(\frac{x_1 - \bar x}{s_x}\right)\left(\frac{y_1 - \bar y}{s_y}\right) + \left(\frac{x_2 - \bar x}{s_x}\right)\left(\frac{y_2 - \bar y}{s_y}\right) + \cdots + \left(\frac{x_n - \bar x}{s_x}\right)\left(\frac{y_n - \bar y}{s_y}\right)\right]r=n−11​[(sx​x1​−xˉ​)(sy​y1​−yˉ​​)+(sx​x2​−xˉ​)(sy​y2​−yˉ​​)+⋯+(sx​xn​−xˉ​)(sy​yn​−yˉ​​)]…

A set of x and y scores has Mx=4,SSx=10,My=5,SSy=40,SP=20.Which is the regress equation for predicting y from x?