Question 1176480
Let's solve this problem step-by-step.

**a. Plot the Data on a Scatter Diagram**

* **X-axis:** Advertising Costs (P1,000)
* **Y-axis:** Sales (P1,000)

Plot the following points:

* (20, 385)
* (40, 400)
* (30, 489)
* (50, 580)
* (25, 410)
* (30, 475)
* (40, 510)
* (35, 500)
* (45, 525)
* (20, 360)
* (25, 420)
* (40, 480)

**b. Find the Equation of the Regression Line**

We need to find the equation of the form ŷ = a + bx, where:

* x = Advertising costs
* y = Sales
* b = slope
* a = y-intercept

First, calculate the necessary sums:

* Σx = 20 + 40 + 30 + 50 + 25 + 30 + 40 + 35 + 45 + 20 + 25 + 40 = 400
* Σy = 385 + 400 + 489 + 580 + 410 + 475 + 510 + 500 + 525 + 360 + 420 + 480 = 5434
* Σx² = 400 + 1600 + 900 + 2500 + 625 + 900 + 1600 + 1225 + 2025 + 400 + 625 + 1600 = 14300
* Σy² = 148225 + 160000 + 239121 + 336400 + 168100 + 225625 + 260100 + 250000 + 275625 + 129600 + 176400 + 230400 = 2499696
* Σxy = (20\*385) + (40\*400) + (30\*489) + (50\*580) + (25\*410) + (30\*475) + (40\*510) + (35\*500) + (45\*525) + (20\*360) + (25\*420) + (40\*480) = 7700 + 16000 + 14670 + 29000 + 10250 + 14250 + 20400 + 17500 + 23625 + 7200 + 10500 + 19200 = 190295
* n = 12 (number of data points)

Now, calculate b (slope):

* b = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)
* b = (12\*190295 - 400\*5434) / (12\*14300 - 400²)
* b = (2283540 - 2173600) / (171600 - 160000)
* b = 109940 / 11600
* b ≈ 9.4776

Next, calculate a (y-intercept):

* a = (Σy - bΣx) / n
* a = (5434 - 9.4776\*400) / 12
* a = (5434 - 3791.04) / 12
* a = 1642.96 / 12
* a ≈ 136.9133

Therefore, the regression equation is:

* ŷ = 136.9133 + 9.4776x

**c. Estimate the Sales if the Advertising Cost is P55,000.00**

* x = 55 (since the advertising cost is in P1,000)
* ŷ = 136.9133 + 9.4776\*55
* ŷ = 136.9133 + 521.268
* ŷ ≈ 658.1813

Therefore, the estimated sales are approximately P658,181.30.