Question 1170692: Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
x is 5 6 3 7 12 10 8 11 13 4 9
y is 7.48 9.16 3.04 10.50 11.84 12.36 11.48 12.28 11.04 5.44 12.10
Need to find y= blink + blinkx ( round two decimal places as needed
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's find the equation of the regression line (y = a + bx) using the given data.
**1. Calculate the Sums**
* Σx = 5 + 6 + 3 + 7 + 12 + 10 + 8 + 11 + 13 + 4 + 9 = 88
* Σy = 7.48 + 9.16 + 3.04 + 10.50 + 11.84 + 12.36 + 11.48 + 12.28 + 11.04 + 5.44 + 12.10 = 106.72
* Σx² = 25 + 36 + 9 + 49 + 144 + 100 + 64 + 121 + 169 + 16 + 81 = 814
* Σxy = (5*7.48) + (6*9.16) + (3*3.04) + (7*10.50) + (12*11.84) + (10*12.36) + (8*11.48) + (11*12.28) + (13*11.04) + (4*5.44) + (9*12.10) = 964.64
* n = 11 (number of data points)
**2. Calculate the Slope (b)**
* b = [n(Σxy) - (Σx)(Σy)] / [n(Σx²) - (Σx)²]
* b = [11(964.64) - (88)(106.72)] / [11(814) - (88)²]
* b = [10611.04 - 9391.36] / [8954 - 7744]
* b = 1219.68 / 1210
* b ≈ 1.008
**3. Calculate the Y-Intercept (a)**
* a = (Σy - b(Σx)) / n
* a = (106.72 - 1.008(88)) / 11
* a = (106.72 - 88.704) / 11
* a = 18.016 / 11
* a ≈ 1.638
**4. Regression Line Equation**
* y = a + bx
* y = 1.64 + 1.01x (rounded to two decimal places)
**5. Scatterplot and Characteristic Ignored**
To understand the characteristic ignored, we need to consider the scatterplot. Here's what we might see:
* **Potential Curvature:** If you were to plot the data, it's possible you'd notice a slight curve in the relationship between x and y, rather than a perfectly straight line. The regression line, by definition, is linear and won't capture any such curvature.
* **Outliers:** There might be one or more data points that deviate significantly from the general trend of the data. These outliers can heavily influence the regression line, but the line itself doesn't indicate their presence.
* **Non-Constant Variance:** The spread of the y-values around the regression line might not be uniform across all x-values. For example, the y-values might be more scattered at higher x-values. This is called heteroscedasticity, and the regression line doesn't account for it.
* **Influential points:** points that strongly affect the slope of the line.
* **Non linear correlation:** If when plotted the data forms a curve, the linear regression line will not be a good fit.
Without actually seeing the scatterplot, the most generally applicable characteristic ignored by the linear regression line is the potential for **curvature** in the data.
**Final Answer:**
* y = 1.64 + 1.01x
* Characteristic ignored: potential curvature in the data.
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