below is the sales experience(in months) and the number of computers sold the the previous month of seven sales people.
Experience 4 12 9 6 10 30 7
Sales 19 42 28 31 39 30 21
Using the Minitab info write the straight line(least squares) equation and the correlation coefficent.
The regression equation is:
sales=27.2+0.252 exp
Predictor Coef SECoef T P
Constant 27.195 5.781 4.70 0.005
Exp. 0.2517 0.4201 0.60 0.575
S=8.97833 R-sq=6.7%
I ran your data through an online calculator and the regression equation looks correct. See below:
7 data pairs (x,y):
( 4.00 , 19.0 ); ( 12.0 , 42.0 ); ( 9.00 , 28.0 ); ( 6.00 , 31.0 ); ( 10.0 , 39.0 ); ( 30.0 , 30.0 ); ( 7.00 , 21.0 );
y = a + bx where:
a= 27.2
b= 0.252
Correlation coefficient:
r = 0.259 (p = 0.575)
To find the straight line (least squares) equation and the correlation coefficient using the Minitab information provided, follow these steps:
1. The regression equation in the form of y = mx + b represents the relationship between the predictor variable (experience) and the response variable (sales). In this case, the regression equation is given as sales = 27.2 + 0.252 * exp.
2. The coefficient values for the regression equation can be found under the "Coef" column in the Minitab output. The constant (b) is 27.195 and the coefficient for the predictor variable (m) is 0.2517. Therefore, the equation becomes sales = 27.195 + 0.2517 * exp.
3. The correlation coefficient (R) indicates the strength and direction of the linear relationship between the two variables. In this case, the correlation coefficient is given as R-sq = 6.7%. The R-squared value represents the percentage of variation in the sales variable that can be explained by the predictor variable.
To summarize:
The straight line (least squares) equation is: sales = 27.195 + 0.2517 * exp
The correlation coefficient (R-squared) is: 6.7%