Question

5. (2 points) When a least-squares linear regression equation is constructed based upon a data set, and a line is constructed from this equation, which (Gif any) of the following is a. The point (F,) must be on the regression line. b. The point (0,b) must be on the regression line. c. The point (0,b) must be on the regression line. d. None of the above statements are false. All of the above statements are true. ons for ss is 6. (2 points) The +/-sign of the corelation coefficient, r, will always match the +/-sign of the slope of the corresponding least-squares linear regression line. TRUE/ FALSE The table below contains eight hours of summarized fast-food restaurant data for the number of walk-in customers for each of eight hours and the number of drive-thru customers for those same hours: 7. Walk-In Customer Count X) 25 18 15 10 23 29 Drive-Thru Customer Hour Count (Y) 20 24 21 20 23 31 16 30 7 24 a) (3 points) Use your calculator to "automatically" generate the least-squares linear regression line for predicting the number of hourly drive-thru customers, given the number of hourly walk-in customers. Write the regression line in the space below, with coefficients accurate to two decimal places. b) (2 points) What fraction of the variation in hourly drive-thru customers(Y) is explained by this particular least-squares regression line that is based on the variation in hourly walk-in customers (X)? In other words, what is the explanatory power of the regression model? Write the value in the space below, rounded to four digits.

Answer 1

5.  b. The point (0,b₀) must be on the regression line.

The above is false.

• Both the mean of x and y $(\bar x, \bar y)$ lie on the regression line as they satisfy the regression equation.
• b1 is the slope intercept, it has to be on the regression line
• b0 is the constant which would not necessarily lie on the regression line.

6. TRUE

The slope of the least square regression line is where it cuts the y axis. If it is positive, there is a upward trend to the line, if it is negative there is downward trend to the line. The sign of the correlation coefficient depends upon whether the line is showing a upward or downward trend. Hence both the signs will always match.