## 9.7 Because of fluctuations in insurance coverage

## 9.7 Because of fluctuations in insurance coverage

9.7 Because of fluctuations in insurance coverage, the average price paid out of pocket (P) by patients of an urgent care center varied, as the table shows. The number of visits per month (Q) also varied, and an analyst believes the two are related. The analyst also thinks the data show a trend. Runa regression of Q on P and Period to test these hypotheses. Then use the estimated parameters a,b, and c and the values of Month and P to predict Q (number of visits.) The prediction equationn is Q = a + (b * Month) + (c *P).

Month | P | Q |

1 | 21 | 193 |

2 | 18 | 197 |

3 | 15 | 256 |

4 | 24 | 179 |

5 | 18 | 231 |

6 | 21 | 214 |

7 | 18 | 247 |

8 | 15 | 273 |

9 | 20 | 223 |

10 | 19 | 225 |

11 | 24 | 198 |

12 | 20 | 211 |

The average price paid out of pocket by patients = (P)

The number of visits per month = (Q)

The prediction equationn is Q = a + (b * Month) + (c *P).

Sample size: 12

Mean x (x̄): 19.416666666667

Mean y (ȳ): 220.58333333333

Intercept (a): 379.59103139014

Slope (b): -8.1892376681615

Regression line equation: y=373.5820044-8.709249622x

Data analysis Results

SUMMARY OUTPUT | ||||||||

Regression Statistics | ||||||||

Multiple R | 0.911589952 | |||||||

R Square | 0.830996241 | |||||||

Adjusted R Square | 0.79343985 | |||||||

Standard Error | 12.65237336 | |||||||

Observations | 12 | |||||||

ANOVA | ||||||||

df | SS | MS | F | Significance F | ||||

Regression | 2 | 7084.173701 | 3542.086851 | 22.12662662 | 0.000335377 | |||

Residual | 9 | 1440.742966 | 160.0825517 | |||||

Total | 11 | 8524.916667 | ||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |

Intercept | 373.5820044 | 25.87757072 | 14.43651757 | 1.57244E-07 | 315.0428724 | 432.1211363 | 315.0428724 | 432.1211363 |

Month | 2.477834739 | 1.073517081 | 2.308146543 | 0.046376973 | 0.049370385 | 4.906299092 | 0.049370385 | 4.906299092 |

P | -8.709249622 | 1.331772881 | -6.539590759 | 0.000106446 | -11.72192918 | -5.696570061 | -11.72192918 | -5.696570061 |