X is a continuous variable that takes on values between 5 and 100. Z is a binary variable. Sketch the following regression functions (with values of X on the horizontal axis): a) Y=2.0+3.0 ́ln(X). b) Y=2.0-3.0 ́ln(X). i) Y =2.0+3.0 ́ln(X)+4.0Z,with Z=1.

Data from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.

A researcher is interested in finding out the factors which determined the yearly spending on family outings last year ​(Y​, measured in​ dollars). She compiles data on the number of members in a family ​(X1​), the annual income of the family ​(X2​), and the number of times the family went out on an outing in the last year ​(X3​). She collects data from 196 families and estimates the following​ regression:   Y=120.45+1.54X1+2.12X2+2.12X3.   Suppose β1​, β2​, β3​, denote the population slope coefficients of X1​, X2​, and X3​, respectively.   The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant​ effect, keeping X3 constant. She calculates the value of the F​-statistic for the test with the two restrictions ​(H0: β1=0, β2=0 vs. H1: β1≠0 and/or β2≠0​) to be 3.00.   The p​-value for the test will be enter your response here?

A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?

The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.8 + 0.3x, +4.5x,, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values for the values of the independent variables. x, = 70, x, = 8.6 The predicted volume is cubic feet. (Round to one decimal place as needed.)

A particular article used a multiple regression model to relate y = yield of hops to x₁ = mean temperature (°C) between date of coming into hop and date of picking and x₂ = mean percentage of sunshine during the same period. The model equation proposed is the following. y = 415.116.6x₁4.50x2+e (a) Suppose that this equation does indeed describe the true relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 39? (b) What is the mean yield when the mean temperature and percentage of sunshine are 19.1 and 42, respectively? You may need to use the appropriate table in Appendix A to answer this question.

Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income:  ŷ =121.09−0.57246xR2=0.894  where y = annual Canada Child Benefit paid (in $100s)           x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid    .The correlation between the two variables is    .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r=    , the relationship is    . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…

Assume there is a positive linear correlation between the variable R (Return rate in percent of a financial investment) and the variable t (age in years of the investment) given by the regression equation R= 2.3t + 4.8  A. Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? B. If the investment continues to grow at a constant rate, what is the expeted return rate when the investment is 7 years old? C. If the investment continues to grow at a constant rate, how old is the investment when the return rate is 30%?