Assignment - 3 Intro to BA

Year Year as number Birthrate 1965 65 19.4 a.) 1970 70 18.4 1975 75 14.8 1980 80 15.9 1985 85 15.6 1990 90 16.4 1995 95 14.8 2000 100 14.4 2005 105 14 2010 110 13 1978 78 16.7397575757576 2012 112 12.9111515151515 2050 150 8.63212121212121 Regression analysis SUMMARY OUTPUT Regression Statistics Multiple R 0.864407483 R Square 0.747200296 Adjusted R Square 0.715600333 Standard Error 1.051679753 Observations 10 ANOVA df Regression 1 Residual 8 Total 9 Coefficients Intercept 25.5230303 X Variable 1 -0.11260606 RESIDUAL OUTPUT Observation Predicted Y 1 18.20363636 2 17.64060606 3 17.07757576 4 16.51454545 60 70 80 0 5 10 15 20 25 f(x) = − 0.1126060606 Scatter p Birthrate

5 15.95151515 6 15.38848485 7 14.82545455 8 14.26242424 9 13.69939394 10 13.13636364 b.) The equation of regression line is: Y = a + bx Here, Y is birthrate a is intercept b is slope of the regression line x is the year as number So the equation is, Birthrate = 25.523030 + (-0.112606 c.) Regression Statistics Multiple R 0.864407483 R Square 0.747200296 Adjusted R Square 0.715600333 Standard Error 1.051679753 Observations 10 d.) Intepret the slope of the line Slope of the line = -0.11260606 e.) Estimte the birthrate for 1978: Estimated birthrate = 25.523030 + ( 16.73975758 Estimated birthrate for 1978 is 16.7 f.) The residual value for 1978 is: Residual = Actual birtharte - Predict Here, Actual birthrate is 15.0 And Predicted birthrate is 16.73975 Residual = -16.7397576 Residual for the year 1978 is -1.7397 g.) Birthrate in 2012: Birthrate in 2012 = 12.91115152 Comment on this prediction: 12.9111515 births are anticipated in Regarding the confidence in this esti making predictions with linear regre The dependent variable (birthrate) a related in linear regression.

SS MS F Significance F 26.15275757576 26.15275758 23.6456067 0.0012515469 8.848242424242 1.106030303 35.001 Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 2.053368349671 12.42983525 1.6388E-06 20.787954398 30.25810621 20.7879543976 30.258106208469 0.023157226013 -4.86267485 0.00125155 -0.16600672 -0.0592054 -0.1660067196 -0.05920540166 Residuals 1.196363636364 0.759393939394 -2.27757575758 -0.61454545455 General trend: Over this period, there generally has been a stead birthrate. Even if the tendency is downward, ther variations from year to year. For example, there are temporary increases in the those observed between 1980 and 1985 and 1990 periods of stability. After the mid-1990s, the birthrate begins to fall m significantly decreases from 16.4 in 1990 to 13.0 i In conclusion, there has been a decline in the birth States overall between 1965 and 2010. Different economic factors, such as changes in fam education, employment options for women, and c have resulted decline in birthrate. 90 100 110 120 606061 x + 25.5230303030303 plot ofBirthrate Year as number

-0.35151515152 1.011515151515 -0.02545454545 0.137575757576 0.300606060606 -0.13636363636 * year as number) (-0.112606 * 78) 7397576 ted birthrate 576 75758 The given data represents the birthrate in different years from 1965 to 2010. The R-squared value is 75%. The statistical measure R-squared (R2) reveals how effectively the line depicts the correlatio between the years and birthrates. A comparatively high R-squared value of 75% indicates that the linear model properly explai the variation in birthrates according to year. In other words, the line effectively depicts the overall pattern or trend in the data. n 2012, according to predictions. timate, it's important to take into account the limitations of ession. and independent variable (year) are assumed to be linearly

dy drop in the re are minor e birthrate (such as 0 and 1995) or more drastically. It in 2010. hrate in the United mily planning, cultural changes that

on ins 75% of