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V. DETERMINING CHILD CARE MARKET RATES Child Care Market Rate Survey 2023 Page | 35

three-star facilities or unusually low rates at the four- and five-star facilities, or any combination of the above. For those counties and age categories, state-level data were substituted for individual- level county data. The procedures used in the multiple regression analysis are detailed below. 1. The county “slopes” (numbers representing the strength of the relationship between star rating and cost) were obtained by regressing the star ratings against the 75th percentile rates for each age category in each county. 2. The regression models were weighted by the number of children at each star level. If there were no children at a star level, the weight was set as 1 in order to include the imputed value in the regression. 3. Even though all imputations were based on more children than the individual category, the imputed rates were determined using the number of children at each star level. It therefore made sense to weight a star rating with many children more than a star rating with few children when performing the regression. Plotting the data would show the star ratings on the X-axis, and the 75th percentile rates on the Y-axis. 4. Three different regressions were performed for each of these graphs: a linear regression (based on star rating), and two nonlinear regressions, one based on the square of the star rating and one based on the cube of the star rating. 5. The curve with the closest fit to the data is used as the county’s slope for each combination of provider type and age category. A curved line (a best-fit for squared or cubed star rating) means that for that age category, the market pays a higher premium for moving from one-star rating to a higher star rating as the star ratings increase; the premium for moving from four- to five-star ratings will be larger than the premium for moving from three-to-four-star ratings. The fitted points are then set as the market rates. 6. For counties and age categories with inverse relationships between star level and rates, an additional step was taken. Three new regression analyses were performed statewide for each type and age category, and as with the county regressions, the closest fit was set as the slope. The mean differences or percent differences for the county’s rate (from the corresponding state rates) were then applied to the state slopes to set a new revised market rate.