The Simple Linear Regression model is       Y = b0 + b1*X1 + u       and the Multiple Linear Regression model with k variables is:       Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u       Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,       Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if:   one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) )     QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity' is violated if:    the model includes two variables that are not correlated the model includes both X1 and X1^2 (i.e. X1-squared) if two of the explanatory variables have a Pearson correlation equal to 0.98 if two of the explanatory variables have a Pearson correlation equal to -1     QUESTION 9 Suppose the estimated MLR model is, Yhat = 2 + 1.5*X1 + 0.5*X2 + 2*X3. Suppose that for an observation with X1=2, X2=-2, X3=5, we observe an actual value in the sample of Y=10. What is the residual, uhat, for this observation?   negative 4 negative 14 positive 4 positive 14

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y = b₁x + bowhere y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the following results were obtained: y = 74.80 + 17.80x Give a practical interpretation of the estimate of the slope of the least squares line. For each additional room in the house, we estimate the appraised value to increase $74,800. For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 17.80 rooms. For a house with O rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the…

The​ least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. In a particular​ region, 28.3 percent of adults 25 years and older have at least a​ bachelor's degree. The median income in this region is ​$37,389. Is this income higher than what you would​ expect? Why?

The​ least-squares regression equation is y=761.7x+13,208 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7483.   Predict the median income of a region in which 20​% of adults 25 years and older have at least a​ bachelor's degree.

The​ least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a​ bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962. Predict the median income of a region in which 25​% of adults 25 years and older have at least a​ bachelor's degree.

The table shows the numbers of new-vehicle sales (in thousands) in the United States for Company A and Company B for 10 years. The equation of the regression line is y = 0.991x + 1,222.81. Complete parts (a) and (b) below. New-vehicle sales (Company A), x New-vehicle sales (Company B), y 4,149 3,923 3,566 3,400 3,266 3,076 2,868 2,485 1,952 2,066 4,912 4,871 4,827 4,721 4,672 4,474 4,684 3,822 2,956 2,754 (a) Find the coefficient of determination and interpret the result. r² = r2 = 0.821 (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? The coefficient of determination is the fraction of the variation in new-vehicle sales for Company B that can be 2 explained by the variation in new-vehicle sales for Company A and is represented by The remaining fraction of the variation, 1-2, is unexplained and is due to other factors or to sampling error. s (b) Find the standard error of estimates and interpret the result. Se O (Round to three decimal…

When the relationship between an independent variable and a dependent variable is assumed to be a straight line what type of regression is it? *   a) Simple linear regression   b) Multiple linear regression   c) Both options A and B   d) None of the above

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The city wants to further develop the model to include the weather conditions of rainy, cloudy, or sunny. Ice Rink Attendance Temperature (°F) Weather Condition 140 45 Sunny 110 40 Cloudy 135 50 Cloudy 120 40 Cloudy 165 45 Sunny 180 45 Sunny 210 50 Sunny 190 45 Cloudy 170 40 Cloudy 130 45 Rainy 140 45 Cloudy 80 35 Rainy 120 45 Cloudy 100 45 Rainy What is the regression equation?  Use the equation to forecast ice rink attendance if the temperature is 38°F and sunny.  Should you keep weather condition in the model?

Data on tuition and mid-career salary are collected from a number of universities and colleges. The result of the data collection is the linear regression model ŷ=0.93x + 167 where x = annual tuition and y = average mid-career salary of graduates, both in thousands of dollars. 1. Which quantity is the independent variable? O average mid-career salary of graduates annual tuition OF 2. According to this model, what is the average salary for a graduate of a college or university where the annual tuition is $30,000? $ 3. What is the slope of this regression model?