Question

1-A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: ?̂=120+5? This implies that if the height is increased by 1 inch, the weight is expected to:
A. increase by 5 pounds
B. increase by 24 pounds
C. increase by 1 pound
D. decrease by 1 pound

If the coefficient of correlation is -0.60, then the coefficient of determination is:
A. 0.36
B. -0.36
C. -0.60
D. 0.40

2- For the equation ?=8.5?−9

a. the y-intercept is?     The slope is ?

3) Is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average (in thousandths) of 8 teams.

Team	Games Won	Batting Average
1	96	274
2	67	282
3	76	288
4	62	265
5	120	273
6	98	286
7	82	288
8	78	268

Using games won as the explanatory variable ?, do the following:

(a) The correlation coefficient is ?=

(b) The equation of the least squares line is ?̂=

Answer 1

Q1a) As the regression equation slope coefficient here is 5, therefore for a unit increase in height, keeping other things constant, we expect an increase in weight by 5 units. Therefore a) increase by 5 pounds is the correct answer here.

Q1b) The coefficient of determination is computed from the correlation coefficient as:

Therefore A) 0.36 is the required value here.

Q2) The regression equation here is:

y = 8.5? − 9

Therefore 8.5 is the slope coefficient here and the intercept is the constant value given as -9 here.

Q3) The given data is inputted in EXCEL and we use the SCATTERPLOT plot to get the scatter plot here. Then we use the TRENDLINE function to get the regression line here as:

a) The correlation coefficient here is computed as:

Therefore 0.051 is the required correlation coefficient here.

b) The equation of the least squares line is given here as: