In a simple linear regression problem, the following statistics are calculated from a sample of 10 observations: $\sum ( x - \bar { x } ) ( y - \bar { y } ) = 2250 , s _ { x } = 10 , \sum x = 50 , \sum y = 75$ . The least squares estimates of the slope and y-intercept are, respectively,
A)1.5 and 0.5
B)2.5 and 1.5
C)1.5 and 2.5
D)2.5 and -5.0

Question

Quizplus · Accepted Answer

The slope $ b_1 $ is calculated as $\frac{\sum ( x - \bar { x } ) ( y - \bar { y } )}{s_x^2}$. Given $ s_x = 10 $, $ s_x^2 = 100 $. So, $ b_1 = \frac{2250}{100} = 22.5 $. The intercept $ b_0 $ is calculated as $\bar{y} - b_1 \bar{x}$. Given $\sum x = 50$, $\sum y = 75$, $\bar{x} = 5$, $\bar{y} = 7.5$. So, $ b_0 = 7.5 - 22.5 \times 5 = -105 $. However, there seems to be a mistake in the calculation or given options, as none match the calculations.

In a Simple Linear Regression Problem, the Following Statistics Are ∑(x−xˉ)(y−yˉ)=2250,sx=10,∑x=50,∑y=75\sum ( x - \bar { x } ) ( y - \bar { y } ) = 2250 , s _ { x } = 10 , \sum x = 50 , \sum y = 75∑(x−xˉ)(y−yˉ​)=2250,sx​=10,∑x=50,∑y=75

In a Simple Linear Regression Problem, the Following Statistics Are $\sum ( x - \bar { x } ) ( y - \bar { y } ) = 2250 , s _ { x } = 10 , \sum x = 50 , \sum y = 75$