Given the linear regression model: Yi = Bo+B1x1 + ẞ2xi2 + Єi, i = 1,..., n Consider the following sums from n = 10 observations on Y, X1, and X2: 10 10 10 Σ3 = 20, Σ i=1 10 Συ? = 98.2, i=1 i=1 10 10 10 71 =0.0, Σ i=1 10 x12 = 0.0 Σαμ = 92, Σα? i=1 = 163 i=1 10 Σ Yixil = 59, Yixi2 = 88, Xi1i2=119 i=1 i=1 i=1 Explore the following steps: 1. Construct the XTX matrix and the vector XTy. 2. Calculate the least-squares estimates of Bo, B₁, and ẞ2, along with the residual sum of squares, SSE. 3. Investigate the hypothesis that the coefficient of X 2, represented by 32, is zero.

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.711 b=30.651 r²-0.670761 r=-0.819 Use this to predict the number of situps a person who watches 10.5 hours of TV can do (to one decimal place)

Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 135 to 190 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.42 cm, y = 81.41 kg, r= 0.193, P-value = 0.054, and y = - 106 + 1.14x. Find %3D the best predicted value of y (weight) given an adult male who is 142 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 142 cm tall is kg. (Round to two decimal places as needed.)

A regression was run to determine if there is a relationship between hours of study per week (xx) and the final exam scores (yy).The results of the regression were: y=ax+b a=6.22 b=21.6 r2=0.477481 r=0.691 Use this to predict the final exam score of a student who studies 8 hours per week, and please round your answer to a whole number.

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: ý = bo + bịx bo = 36.465 - 1.082 b1 - 0.646 Use this to predict the number of situps a person who watches 2.5 hours of TV can do (to one decimal place)

The following estimated regression equation is based on 10 observations was presented. Here SST = 6,718.875, SSR = 6,016.125, sb = 0.0861, and Sb₂ = 0.0531. a. Compute MSR and MSE (to 3 decimals). MSR = MSE = b. Compute F and perform the appropriate F test (to 2 decimals). Use a = 0.05. Use the F table. F = The p-value is - Select your answer At a = 0.05, the overall model is Select your answer - c. Perform a t test for the significance of B₁ (to 2 decimals). Use α = 0.05. Use the t table. to₁ = The p-value is - Select your answer At a = 0.05, there is - Select your answer-relationship between y and 1. d. Perform a t test for the significance of ₂ (to 2 decimals). Use a = 0.05. Use the t table. to₂ = The p-value is - Select your answer At a = 0.05, there is - Select your answer - relationship between y and 2. ŷ = 29.1270 +0.5906x1 +0.4980x2

For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the heights (ft) of the eruptions. The linear correlation coefficient is r = 0.0915 and the regression equation is  = 119 + 0.0331x, where x represents duration time. The mean of the 40 duration times is 245.0 sec and the mean of the 40 heights is 127.2 ft. What is the best predicted height of an eruption with a duration time of 120 min?

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=a+bx a=37.5 b=-1.319 r2=0.597529 r=-0.773 Assume the correlation is significant (p-value < α α ), and use this to predict the number of situps a person who watches 7.5 hours of TV can do (to one decimal place)

In multiple regression analysis involving 10 independent variables and 100 observations, the critical value tt for testing individual coefficients in the model will have:A. 10 degrees of freedomB. 89 degrees of freedomC. 100 degrees of freedomD. 9 degrees of freedom In a multiple regression analysis involving 40 observations and 5 independent variables, the total variation SST=350 and SSE=50. The multiple coefficient of determination is:A. 0.8469B. 0.8529C. 0.8408D. 0.8571

Find the correlation coefficient given the estimated regression equation = 25+6x and ² = .8754.